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p-Kirchhoff型方程解的多重性 被引量：3

Multiplicity of Solution of p-Kirchhoff Type Equation
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摘要 考虑p-Kirchhoff型方程解的多重性.应用变分法,结合非线性项在零点和无穷远处的渐近性态,当Ambrosetti-Rabinowitz条件不满足时得到了p-Kirchhoff型方程解的存在性. This paper deals with the multiplicity of solutions of p-Kirchhoff type equations.With the help of the variational method,together with the asymptotic behavior of the nonlinearity at zero and infinity,the existence of the solution of p-Kirchhoff type equation is established when the Ambrosetti-Rabinowitz condition is not required.
作者 李健 杜泊船 赵昕 吕显瑞
机构地区 吉林农业大学信息技术学院 吉林大学生命科学学院 吉林大学数学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2013年第4期580-584,共5页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11071026) 吉林省自然科学基金(批准号:201215038 201215184)
关键词 变分法 正解 负解 p-Kirchhoff型方程 生物种群密度 variational method positive solution negative solution p-Kirchhoff type equation biological population density
分类号 O175.25 [理学—基础数学] O177 [理学—基础数学]
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参考文献11

  • 1Kirchhoff G. Mechanik [M]. I.eipzig: Teubner, 1883.
  • 2CHENG Bi-tao, WU Xian, LIU Jun. Multiple Solutions for a Class of Kirchhoff Type Problems with Concave Nonlinearity [J]. Nonlinear Differ Equ Appl, 2012, 19(5): 521- 537.
  • 3MAO An-min, ZHANG Zhi-tao. Sign-Changing and Muhiple Solutions of Kirchhoff Type Problems without the P.S. Condition [J]. Nonlinear Anal: Theory, Methods -. Applications, 2009, 70(3): 1275-1287.
  • 4Perera K, ZHANG Zhi tao. Nontrivial Solutions of Kircbhoff-Type Problems via the Yang Index [J]. J Differential Equations, 2006, 221(1): 246-255.
  • 5Correa F J S A, Figueiredo G M. On an Elliptic Equation of p-Kirchhoff Type via Variational Methods [J]. Bull Austral Math Soc, 2006,74(2):263-277.
  • 6Correa F J S A, Figueiredo G M. On a p-Kirchhoff Equation via Krasnoselskii's Genus [J]. Appl Math Letl, 2009, 22(6): 819- 822.
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  • 8LIU Du-chao, ZHAO Pei-hao. Multiple Nontrivial Solutions to a p-Kirchhoff Equation [J]. Nonlinear Anal: Theory, Methods & Applications, 2012, 75(13): 5032-5038.
  • 9Gasiflski L, Papageorgiou N S. Multiple Solutions for Asymptotically (p- 1 )-Homogeneous p-Laplacian Equations [J]. J Funct Anal, 2012, 262(5): 2403-2435.
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同被引文献24

  • 1Correa FJ S A, Figueiredo G M. On an Elliptic Equation of p-Kirchhoff Type via Variational Methods[J]. Bull Austral Math Soc, 2006, 74(2): 263-277.
  • 2Correa FJ S A, Figueiredo G M. On a p-Kirchhoff Equation via Krasnoselskii' s Genus[J]. Appl Math Lett, 2009, 22(6): 819-822.
  • 3Harnydy A, Massar M, Tsouli N. Existence of Solutions for p-Kirchhoff Type Problems with Critical Exponent[J]. ElectronJ Differential Equations, 2011, 2011( 105): 1-8.
  • 4LIU Duchao , ZHAO Peihao. Multiple Nontrivial Solutions to a p-Kirchhoff Equation[J]. Nonlinear Analysis: Theory, Methods &. Applications, 2012, 75(3): 5032-5038.
  • 5Kirchhoff G. Mechanik[M]. Leipzig, German: Teubner, 1883.
  • 6Gasinski L, Papageorgiou N S. Multiple Solutions for Asymptotically (p - 1 )-Homogeneous p-Laplacian Equations[J].J Funct Analysis: Theory, Methods &. Applications, 2012, 262(5): 2403-2435.
  • 7au Zengqi , LI Chun, Existence of Solutions for Dirichlet Problems with p-Laplacian[J]. Nonlinear Analysis: Theory, Methods &. Applications, 2012, 75(13): 4914-4919.
  • 8SHI Linsong , CHANG Xiaojun. Multiple Solutions to p-Laplacian Problems with Concave Nonlinearities[J]. J Math Anal Appl , 2010, 363(1): 155-160.
  • 9Rabinowitz P H. Minimax Methods in Critical Point Theory with Applications to Differential Equations[M]. Washington D C: American Mathematical Society, 1986.
  • 10Kirchhoff G. Mechanik [M]. Leipzig: Teubner,1883.

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吉林大学学报（理学版）
2013年 第4期

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