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内藤 雄基ナイトウ ユウキ

所属部署
大学院理工学研究科 数理物質科学専攻
職名教授
メールアドレスnaito.yuki.mu[at]ehime-u.ac.jp ※[at]を@に書き換えて送信して下さい
ホームページURL
生年月日
Last Updated :2017/08/18

研究者基本情報

学歴

  •  - 1989年, 広島大学, 理学研究科, 数学専攻
  •  - 1990年, 広島大学, 理学研究科, 数学専攻
  •  - 1987年, 広島大学, 理学部, 数学科

経歴

  •   2009年, - 愛媛大学理工学研究科
  •   2007年,  - 2009年,  神戸大学大学院工学科
  •   1999年,  - 2007年,  神戸大学工学部
  •   1996年,  - 1999年,  神戸大学工学部
  •   1990年,  - 1996年,  広島大学理学部

所属学協会

  • 日本数学会
  • 日本応用数理学会

研究活動情報

研究キーワード

    非線形偏微分方程式

MISC

  • A priori bounds for superlinear elliptic equations with semidefinite nonlinearity
    Yūki Naito, Takashi Suzuki, Yohei Toyota, Nonlinear Analysis, Theory, Methods and Applications, 151,   2017年03月01日, © 2016 The Author(s)We derive a priori bounds for positive solutions of the superlinear elliptic problems −Δu=a(x)up on a bounded domain Ω in RN, where a(x) is Hölder continuous in Ω. Our main motivation is to study the case where a(x)≥0, a(x)≢0 and a(x) has some zero sets in Ω. We show that, in this case, the scaling arguments reduce the problem of a priori bounds to the Liouville-type results for the equation −Δu=A(x')up in RN, where A is the continuous function defined on the subspace Rk with 1≤k≤N and x'∈Rk. We also establish a priori bounds of global nonnegative solutions to the corresponding parabolic initial–boundary value problems.
  • A remark on self-similar solutions for a semilinear heat equation with critical Sobolev exponent
    内藤 雄基, Advanced Studies in Pure Mathematics, 64,   2015年
  • Existence and separation of positive radial solutions for semilinear elliptic equations
    Soohyun Bae, Yuki Naito, Journal of Differential Equations, 257,   2014年10月01日, We consider the semilinear elliptic equation δu+K(|x|)up=0 in RN for N>2 and p>1, and study separation phenomena of positive radial solutions. With respect to intersection and separation, we establish a classification of the solution structures, and investigate the structures of intersection, partial separation and separation. As a consequence, we obtain the existence of positive solutions with slow decay when the oscillation of the function r-ℓK(r) with ℓ>-2 around a positive constant is small near r=∞ and p is sufficiently large. Moreover, if the assumptions hold in the whole space, the equation has the structure of separation and possesses a singular solution as the upper limit of regular solutions. We also reveal that the equation changes its nature drastically across a critical exponent pc which is determined by N and the order of the behavior of K(r) as r=|x|→0 and ∞. In order to understand how subtle the structure is on K at p=pc, we explain the criticality in a similar way as done by Ding and Ni (1985) [6] for the critical Sobolev exponent p=(N+2)/(N-2). © 2014 Elsevier Inc..
  • Global attractivity and convergence rate in the weighted norm for a supercritical semilinear heat equation
    内藤 雄基, Differential Integral Equations , 28,   2015年
  • Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity
    Yūki Naito, Kodai Mathematical Journal, 37,   2014年01月01日, © 2014, Tokyo Institute of Technology. All rights reserved. We study the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. It is known that two solutions approach each other if these initial data are close enough near the spatial infinity. In this paper, we give its sharp convergence rate in the weighted norms for a class of initial data. Proofs are given by a comparison method based on matched asymptotics expansion.
  • Characterization for rectifiable and nonrectifiable attractivity of nonautonomous systems of linear differential equations
    Yuki Naito, Mervan Pašić, International Journal of Differential Equations, 2013,   2013年11月21日, We study a new kind of asymptotic behaviour near t = 0 for the nonautonomous system of two linear differential equations: x ' (t) = A (t) x (t), t ε (0, t0], where the matrix-valued function A = A (t) has a kind of singularity at t = 0. It is called rectifiable (resp., nonrectifiable) attractivity of the zero solution, which means that || x (t) ||2 → 0 as t → 0 and the length of the solution curve of x is finite (resp., infinite) for every x ≠ 0. It is characterized in terms of certain asymptotic behaviour of the eigenvalues of A (t) near t = 0. Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at t = 0. © 2013 Yūki Naito and Mervan Pašić.
  • Bounded and unbounded oscillating solutions to a parabolic-elliptic system in two dimensional space
    Yuki Naito, Takasi Senba, Communications on Pure and Applied Analysis, 12,   2013年09月01日, In this paper, we consider solutions to a Cauchy problem for a parabolic-elliptic system in two dimensional space. This system is a simplified version of a chemotaxis model, and is also a model of self-interacting particles. The behavior of solutions to the problem closely depends on the L1-norm of the solutions. If the quantity is larger than 8π, the solution blows up infinite time. If the quantity is smaller than the critical mass, the solution exists globally in time. In the critical case, infinite blowup solutions were found. In the present paper, we direct our attention to radial solutions to the problem whose L1-norm is equal to 8π and find bounded and unbounded oscillating solutions.
  • The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations
    Yuki Naito, Journal of Differential Equations, 253,   2012年12月01日, We consider the Cauchy problem, where N>2, p>1, and u 0 is a bounded continuous non-negative function in R N. We study the case where u 0(x) decays at the rate |x| -2/(p-1) as |x|→∞, and investigate the stability and instability properties of forward self-similar solutions. In particular, we obtain optimal conditions on the initial function u 0 for the global existence in terms of self-similar solutions, and show the asymptotically self-similar behavior of the global solutions. We also obtain the condition for finite time blow-up by making use of the behavior of u 0(x) as |x|→∞. © 2012 Elsevier Inc.
  • Blow-up behavior of solutions to a parabolic-elliptic system on higher dimensional domains
    Yuki Naito, Takasi Senba, Discrete and Continuous Dynamical Systems, 32,   2012年07月12日, We consider a parabolic-elliptic system of equations that arises in modelling the chemotaxis in bacteria and the evolution of self-attracting clusters. In the case space dimension 3 ≤ N ≤ 9, we will derive criteria of the blow-up rate of solutions, and identify an explicit class of initial data for which the blow-up is of self-similar rate. Our argument is based on the study of the asymptotic properties of backward self-similar solutions to the system together with the intersection comparison principle.
  • Classification of second-order linear differential equations and an application to singular elliptic eigenvalue problems
    Yuki Naito, Bulletin of the London Mathematical Society, 44,   2012年06月01日, We consider conditionally oscillatory second-order linear differential equations with a parameter, and investigate the asymptotic behaviour and number of zeros of solutions to the equations. In particular, we find criteria for the equations to be oscillatory/nonoscillatory when the parameter is on the oscillation constant. We also show an application to singular elliptic eigenvalue problems on a ball in R N. © 2012 London Mathematical Society.
  • Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent
    Yuki Naito, Tokushi Sato, Annali di Matematica Pura ed Applicata, 191,   2012年01月01日, We consider the non-homogeneous critical semilinear elliptic problems where Ω is a bounded smooth domain in R N, f ε H -1 (ω), f ≥ 0 in Ω, ε R is a fixed constant, and λ > 0 is a parameter. We investigate the multiplicity of positive solutions to the problem and find the phenomenon depending on the space dimension N. Precisely, we show that the situation is drastically different between the cases N = 3, 4, 5 and N ≥ 6 if κ > 0. Our proofs are based on the variational methods and Pohozaev type argument. © 2010 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
  • Oscillating solutions to a parabolic-elliptic system related to a chemotaxis model
    Yuki Naito, Takasi Senba, Discrete and Continuous Dynamical Systems- Series A,   2011年09月01日, In this paper, we consider solutions to a Cauchy problem for a parabolic-elliptic system in two dimensional space. This system is a simplified version of a chemotaxis model, and is also a model of self-interacting particles. The behavior of solutions to the problem closely depends on the L1-norm of the solutions. If the quantity is larger than 8π, the solution blows up in finite time. If the quantity is smaller than the critical mass, the solution exists globally in time. In the critical case, infinite blowup solutions are found. In the present paper, we direct our attention to radial solutions to the problem whose L1-norm is equal to 8π and find oscillating solutions.
  • Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian
    Yuki Naito, Mathematica Bohemica, to appear,   2011年06月23日, We consider the boundary value problem involving the one dimensional p- Laplacian, and establish the precise intervals of the parameter for the existence and nonexistence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.
  • Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent
    SpringerAnn. Mat. Pura Appl., to appear,   2011年
  • Conditional oscillation for second order linear differential equations (New Developments of Functional Equations in Mathematical Analysis)
    内藤 雄基, 数理解析研究所講究録, 1702,   2010年08月
  • Self-similar blow-up for a chemotaxis system in higher dimensional domains (Mathematical analysis on the self-organization and self-similarity)
    NAITO Yuki, SENBA Takasi, 数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu, 15,   2009年12月
  • Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian
    Yuki Naito, Satoshi Tanaka, Nonlinear Anal. TMA, 69, (9) 3070 - 3083,   2008年11月01日, We consider the boundary value problem involving the one-dimensional p-Laplacian (| u′ |p - 2 u′)′ + a (x) f (u) = 0, 0 < x < 1, u (0) = u (1) = 0, where p > 1. We establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f (s) / sp - 1 at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations. © 2007 Elsevier Ltd. All rights reserved.
  • Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent (Variational Problems and Related Topics)
    内藤 雄基, 佐藤 得志, 数理解析研究所講究録, 1671,   2009年12月
  • Self-similar blow-up for a chemotaxis system in higher dimensional domains
    RIMS Kokyuroku BessatsuMathematical analysis on the self-organization and self-similarity, B15,   2009年
  • Self-similar solutions for a semilinear heat equation with critical Sobolev exponent
    Yuki Naito, Indiana Univ. Math. J., 57, (3) 1283 - 1315,   2008年08月21日, The Cauchy problem for a semilinear heat equation with singular initial data (Equation Presented) is studied, where N>2,p = (N + 2) / (N - 2), λ > O is a parameter, and a ≥ 0, a ≄ 0. We show that there exists a constant λ* > 0 such that the problem has at least two positive self-similar solutions for λ ∈ (0,λ*) when N = 3,4,5, and that, when N ≥ 6 and a ≡ 1, the problem has a unique positive radially symmetric self-similar solution for λ ∈ (0, λ* ) with some λ* ∈ (0, λ* ). Our proofs are based on the variational methods and Pohozaev type arguments to the elliptic problem related to the profiles of self-similar solutions.
  • Positive solutions for semilinear elliptic equations with singular forcing terms
    Yuki Naito, Tokushi Sato, J. Differential Equations J. Differential Equations, 235, (2) 439 - 483,   2007年04月15日, We consider the existence of solutions to the semilinear elliptic problem(*)κ{(- Δ u + u = up + κ ∑i = 1 m ci δai in  D′ (RN),; u > 0 a.e. in RN and u (x) → 0 as | x | → ∞,). with prescribed given finite points {ai}i = 1 m in RN and positive numbers {ci}i = 1 m, where N ≥ 3, 1 < p < N / (N - 2), κ ≥ 0 is a parameter, and δa is the Dirac delta function supported at a ∈ RN. We reduce the problem (*)κ to the problem in H1 (RN) ∩ C0 (RN) in terms of auxiliary functions, and then show the existence of a positive constant κ* > 0 such that (*)κ has at least two solutions if κ ∈ (0, κ*), a unique solution if κ = κ*, and no solution if κ > κ*. © 2007 Elsevier Inc. All rights reserved.
  • Self-Similarity in Chemotaxis Systems
    Colloq. Math., 111, (1) 11 - 34,   2008年
  • Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity
    Yuki Naito, Takashi Suzuki, J. Differential Equations, 232, (1) 176 - 211,   2007年01月01日, We consider the blowup rate of solutions for a semilinear heat equationut = Δ u + | u |p - 1 u, x ∈ Ω ⊂ RN, t > 0, with critical power nonlinearity p = (N + 2) / (N - 2) and N ≥ 3. First we investigate the profiles of backward self-similar solutions by making use of the variational method, and then, by employing the intersection comparison argument with a particular self-similar solution, we derive the criteria of the blowup rate of solutions, assuming the positivity of solutions in backward space-time parabola. In particular, we show the existence of the so-called type II blowup solutions for the Cauchy-Dirichlet problems on suitable shrinking domains in the case N = 3. © 2006 Elsevier Inc. All rights reserved.
  • Positive solutions for semilinear elliptic equations involving Dirac measures(Functional Equations Based upon Phenomena)
    内藤 雄基, 佐藤 得志, 数理解析研究所講究録, 1547,   2007年04月
  • An ODE approach to the multiplicity of self-similar solutions for semilinear heat equations
    Yuki Naito, Proc. Roy. Soc. Edinburgh Sect. A, 136, (4) 807 - 835,   2006年09月11日, The Cauchy problem for semi-linear heat equations with singular initial data wt = wp + wp in ℝN × (0, ∞) and w(x, 0) = ℓ|x|-2/(p-1) in ℝ N \ {0}, is studied, where N >2, p > (N + 2)/N, and ℓ > 0 is a parameter. We establish the existence and multiplicity of positive self-similar solutions for the problem by applying the ordinary differential equation shooting method to the corresponding spatial profile problem. © 2006 The Royal Society of Edinburgh.
  • A variational approach to self-similar solutions for semilinear heat equations
    Advanced Studies in Pure Mathematics, Asymptotic Analysis and Singuralities, 47, (2) 675 - 688,   2007年
  • Existence of solutions with prescribed numbers of zeros of boundary value problems for ordinary differential equations with the one-dimensional $p$-Laplacian(Dynamics of functional equations and numerical simulation)
    田中 敏, 内藤 雄基, 数理解析研究所講究録, 1474,   2006年02月
  • Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data
    Yuki Naito, Math. Ann., 329, (1) 161 - 196,   2004年05月01日, The Cauchy problem for semilinear heat equations with singular initial data wt = Δw + wp in RN × (0, ∞) and w(x, 0) = λa (x/|x|) |x|-2/(p-1) in RN \ {0} is studied, where N ≥ 2, λ > 0 is a parameter, and a > 0, a ≢ 0. We show that when p > (N + 2)/N and (N - 2)p < N + 2, there exists a positive constant λ̄ such that the problem has two positive self-similar solutions wλ and w̄ λ with wλ < w̄λ if λ ∈ (0, λ̄) and no positive self-similar solutions if λ > λ̄. Furthermore, for each fixed t > 0, w λ (·,t) → 0 and w̄λ (·,t) → w0(·,t) in L∞ (RN) as λ → 0, where w0 is a non-unique solution to the problem with zero initial data, which is constructed by Haraux and Weissler.
  • Self-similar solutions to a nonlinear parabolic-elliptic system
    Yuki Naito, Takashi Suzuki, Taiwanese J. Math., 8, (1) 43 - 55,   2004年12月01日, We study the forward self-similar solutions to a parabolic-elliptic system ut = Δu - ∇ · (u∇v), 0 = Δv + u in the whole space R2. First it is proved that self-similar solutions (u, v) must be radially symmetric about the origin. Then the structure of the set of self-similar solutions is investigated. As a consequence, it is shown that there exists a self-similar solution (u, v) if and only if ||u|| L1(R2) < 8π, and that the profile function of u forms a delta function singularity as ||u||L1(R2) → 8π.
  • Asymptotically self-similar solutions for the parabolic systems modelling chemotaxis
    Banach Center Publ.Self-similar solutions of nonlinear PDE,, 74,   2006年
  • On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations
    Yuki Naito, Satoshi Tanaka, Nonlinear Anal. TMA, 56, (6) 919 - 935,   2004年03月01日, We consider the boundary value problem for nonlinear second-order differential equations of the form u″ + a(x)f(u) = 0, 0 < x < 1, u(0) = u(1) = 0. We establish the precise condition concerning the behavior of the ratio f(s)/s at infinity and zero for the existence of solutions with prescribed nodal properties. Then we derive the existence and the multiplicity of nodal solutions to the problem. Our argument is based on the shooting method together with the Strum's comparison theorem. The results obtained here can be applied to the study of radially symmetric solutions of the Dirichlet problem for semilinear elliptic equations in annular domains. © 2003 Elsevier Ltd. All rights reserved.
  • Self-similar solutions to a parabolic system modeling chemotaxis
    Yuki Naito, Takashi Suzuki, Kiyoshi Yoshida, J. Differential Equations, 184, (2) 386 - 421,   2002年09月20日, We study the forward self-similar solutions to a parabolic system modeling chemotaxis ut = ∇ · (∇u - u∇v), τvt = Δv + u in the whole space ℝ2, where τ is a positive constant. Using the Liouville-type result and the method of moving planes, it is proved that self-similar solutions (u, v) must be radially symmetric about the origin. Then the structure of the set of self-similar solutions is investigated. As a consequence, it is shown that there exists a threshold in ∫ℝ2 u for the existence of self-similar solutions. In particular, for 0<τ ≤1/2, there exists a self-similar solution (u,v) if and only if ∫ℝ2 u<8π. © 2002 Elsevier Science (USA).
  • Structure of positive self-similar solutions to semilinear heat equations with supercritical nonlinearity (関数方程式と数理モデル 研究集会報告集)
    内藤 雄基, 数理解析研究所講究録, 1309,   2003年02月
  • Oscillation criteria for quasilinear elliptic equations
    Yuki Naito, Hiroyuki Usami, Nonlinear Anal. TMA, 46, (5) 629 - 652,   2001年12月01日
  • Non-uniqueness in the Cauchy problems for semilinear heat equations with singular initial data〔和文〕 (関数方程式の解のダイナミクスとその周辺 研究集会報告集)
    内藤 雄基, 数理解析研究所講究録, 1254,   2002年04月
  • Symmetry results for semilinear elliptic equations in R^2
    Y. Naito, Y. Naito, Nonlinear Anal. TMA 47(6) (2001) 3661-3670, 47, (6) 3661 - 3670,   2001年08月01日, The radial symmetry of classical solutions for semilinear elliptic equations is studied. An approach based on the maximum principle in unbounded domains together with the method of moving plates is presented. This approach helps to develop arguments and simplify the proofs.
  • Some remarks on the method of moving planes〔和文〕 (非線形偏微分方程式の解の構造とその解析手法についての研究)
    内藤 雄基, 数理解析研究所講究録, 1204,   2001年04月
  • Existence of self-similar solutions to a parabolic system modelling chemotaxis
    Naomi Muramoto, Yuki Naito, Kiyoshi Yoshida, Japan J. Indust. Appl. Math., 17, (3) 427 - 451,   2000年10月01日, We investigate a semilinear elliptic equation (SE) -△v - ε/2x · ▽v = λe-1/4|x|2 ev in R2 with a parameter λ > 0 and a constant 0 < ε < 2, and obtain a structure of the pair (λ, v) of a parameter and a solution which decays at infinity. This equation arises in the study of self-similar solutions for the Keller-Segel system. Our main results are as follows: (i) There exists a λ* > 0 such that if 0 < λ < λ*, (SE) has two distinct solutions v + (Combining low line)λ and v̄λ satisfying v + (Combining low line)λ < v̄λ, and that if λ > λ*, (SE) has no solution. (ii) If λ = λ* and 0 < ε < 1, (SE) has the unique solution v*; (iii) The solutions v + (Combining low line)λ and v̄λ are connected through v*.
  • Self-similar solutions to a parabolic system modelling chemotaxis (非線形発展方程式とその応用)
    内藤 雄基, 鈴木 貴, 吉田 清, 数理解析研究所講究録, 1197,   2001年04月
  • Nonexistence results of positive solutions for semilinear elliptic equations in R^n
    Yuki Naito, J. Math. Soc. Japan, 52, (3) 637 - 644,   2000年07月01日, We consider the global properties of nonnegative solutions of the semilinear elliptic equations in the entire space. By employing Pohozaev identity in the entire space and the results concerning the asymptotic behavior of nonnegative solutions, we establish some theorems of Liouville type.
  • Radial symmetry of self-similar solutions for semilinear heat equations
    Yuki Naito, Takashi Suzuki, J. Differential Equations, 163, (2) 407 - 428,   2000年05月20日, The symmetry properties of positive solutions of the equation Δu+1/x · ∇u+ 1/p-1 u + up = 0 in Rn, where n ≥ 2, p > (n + 2)/n, was studied. It was proved that u must be radially symmetric about the origin provided u(x) = o(|x|-2/(p-1)) as \x\ → ∞, and that there exist non-radial solutions u satisfying lim sup|x| → ∞ |x\2/(p-1)u(x) > 0. © 2000 Academic Press.
  • Keller-Segel方程式系に対する自己相似解 (数理モデルと関数方程式)
    村本 直己, 内藤 雄基, 吉田 清, 数理解析研究所講究録, 1128,   2000年01月
  • A note on the moving sphere method
    Yuki Naito, Takashi Suzuki, Pacific J. Math., 189, (1) 107 - 115,   1999年05月01日, We treat the Dirichlet problem for elliptic equations on annular regions, and show the monotonicity and symmetry properties of positive solutions with respect to the sphere. We generalize the argument of the method of moving spheres to more general partial differential equations.
  • Radial symmetry of positive solutions for semilinear elliptic equations in R^n
    Journal of the Korean Mathematical Society, 37, (5) 751 - 761,   2000年
  • Radial symmetry of self-similar solutions for semilinear heat equations (Methods and Applications for Functional Equations)
    内藤 雄基, 鈴木 貴, 数理解析研究所講究録, 1083,   1999年02月
  • Radial symmetry of positive solutionsfor semilinear elliptic equations on the unit ball in R^n
    Funkcial. Ekvac., 41, (2) 215 - 234,   1998年
  • Oscillation and nonoscillation criteria for second order quasilinear differential equations
    T. Kusano, Y. Naito, Acta Math. Hungarica, 76, (1-2) 81 - 99,   1997年07月01日
  • A note on radial symmetry of positive solutions for semilinear elliptic equations in R^n
    Differential Integral Equations, 11, (6) 835 - 845,   1998年
  • Nonexistence results of positive entire solutions for quasilinear elliptic inequalities
    Yuki Naito, Hiroyuki Usami, Canadian Mathematical Bulletin, 40,   1997年06月01日, This paper treats the quasilinear elliptic inequality div(|Du|m-2 Du) ≥ p(x)uσ, x ∈ ℝN, where N ≥ 2, m > 1, σ > m - 1, and p:ℝN → (0, ∞) is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When p has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results.
  • Entire solutions of the inequality div(A(|Du|)Du)≧f(u)
    Yuki Naito, Hiroyuki Usami, Math. Z., 225, (1) 167 - 175,   1997年05月01日
  • Oscillation theory for semilinear elliptic equations with arbitrary nonlinearities
    Funkcial. Ekvac., 40, (1) 41 - 55,   1997年
  • Nonexistence results of positive enitre solutions for quasilinear elliptic equations
    Canad. Math. Bull., 40, (2) 244 - 253,   1997年
  • Radial symmetry of positive solutionsfor semilinear elliptic equations in a disc
    Hiroshima Math. J., 26, (3) 531 - 545,   1996年
  • Damped oscillation of solutions for some nonlinear second order ordinary differential equations
    Adv. Math. Sci. Appl., 5, (1) 239 - 248,   1995年
  • A note on the existence of nonoscillatory solutions of neutraldifferential equations
    Hiroshima Math. J., 25, (3) 513 - 518,   1995年
  • Uniqueness of positive solutions of quasilinear differential equations
    Differential and Integral Equations, 8, (7) 1813 - 1822,   1995年
  • Solutions with prescribed numbers of zeros for nonlinear second order differential equations
    Funkcial. Ekvac., 37, (3) 505 - 520,   1994年
  • Existence and asymptotic behavior of positive solutions of neutral differential equations
    J. Math. Anal. Appl., 188, (1) 227 - 244,   1994年
  • Bounded solutions with prescribed numbers of zeros for the Emden-Fowler differential equation
    Hiroshima Math. J., 24, (1) 177 - 220,   1994年
  • Strong oscillation and nonoscillation of quasilinear differential equations of second order
    Differential Equations and Dynamical Systems, 2, (1) 1 - 10,   1994年
  • Radial entire solutions of a class of sublinear elliptic equations
    Adv. Math. Sci. Appl., 21, (1) 231 - 243,   1993年
  • Asymptotic behavior of decaying nonoscillatory solutions of neutral differential equations
    Funkcial. Ekvac., 35, (1) 95 - 110,   1992年
  • Nonoscillatory solutions of neutral differential equations
    Hiroshima Math. J., 20, (2) 231 - 258,   1990年

書籍等出版物

講演・口頭発表等

  • Separation structure of solutions for elliptic equations with exponential nonlinearity
    内藤 雄基, Nonlinear PDE and Applications,KAIST, Korea,   2017年03月30日, 招待有り
  • Incomplete blow-up of solutions for semilinear heat equations with supercritical nonlinearity
    内藤 雄基, 第34回九州における偏微分方程式研究集会,   2017年02月01日, 招待有り
  • Asymptotic self-similarity of solutions to semilinear heat equations
    内藤 雄基, Mathematical Analysis on Nonlinear PDEs 東北大学,   2017年01月06日, 招待有り
  • Singular extremal solutions for supercritical elliptic equations in a ball
    内藤 雄基, 常微分方程式の定性的理論ワークショップ 島根大学,   2016年09月22日, 招待有り
  • A priori bounds for superlinear ellitptic equations with semidefinite nonlinearity
    鈴木貴、豊田洋平、内藤雄基, 日本数学会秋期大会、関西大学,   2016年09月15日
  • Peaking solutions to semilinear heat equations with supercritical nonlinearities
    内藤 雄基, 7th Euro-Japanese Workshop on Blow-up, Poznun, Poland ,   2016年09月08日, 招待有り
  • Classification of bifurcation diagrams for supercritical elliptic equations in a ball
    内藤 雄基, 第141回神楽坂解析セミナー,   2016年05月28日, 招待有り
  • Structure of positive solutions for semilinear elliptic equations with supercritical growth
    内藤 雄基, 第5回弘前非線形方程式研究会,   2015年12月12日, 招待有り
  • Structure of positive solutions for semilinear elliptic equations with supercritical growth
    内藤 雄基, RIMS 研究集会「偏微分方程式の解の形状と諸性質」,   2015年11月11日, 招待有り
  • Global attractivity in the weighted norm for a supercritical semilinear heat equation
    内藤 雄基, 日本数学会秋期総合分科会(京都産業大学),   2015年09月15日
  • Separation structure of positive radial solutions for semilinear elliptic equations
    内藤 雄基, Equadiff 2015 (Lyon, France),   2015年07月07日
  • Some remarks on separation property of solutions for elliptic equations with exponential nonlinearity
    内藤 雄基, 2015 International Workshop on Nonlinear PDE and Application,   2015年06月12日, 招待有り
  • Threshold solutions for semilinear heat equations with polynomial decay initial data
    内藤 雄基, ひこね解析セミナー ,   2015年06月06日, 招待有り
  • Threshold solutions for semilinear heat equations with polynomial decay initial data
    内藤 雄基, 東北大学 応用数学セミナー,   2015年05月21日, 招待有り


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