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带有凹凸非线性项的重调和方程的多解性 被引量：1

Multiple Solutions for Biharmonic Equations with Concave-Convex Nonlinearities
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摘要 该文研究了一类带有凹凸非线性项以及变号权函数的重调和方程,使用Nehari流形方法证明了该方程具有两个解. In this paper, we consider biharmonic equations involving concave-convex nonlinearities and sign-changing weight function. With the help of Nehari manifold, we prove the existence of two solutions for the biharmonic equation.
作者 张亚静
机构地区 山西大学数学科学学院太原
出处 《数学物理学报（A辑）》 CSCD 北大核心 2013年第2期354-365,共12页 Acta Mathematica Scientia
基金 山西省自然科学基金(2009011008) 山西省回国留学人员科研项目(2011-005) 山西省高等学校优秀青年学术带头人支持计划资助
关键词 重调和方程 凹凸非线性项 NEHARI流形 Biharmonic equations Concave-convex nonlinearities Nehari manifold.
分类号 O175.2 [理学—基础数学]
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参考文献11

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  • 1Astrita G, Marrucci G. Principles of Non-Newtonian Fluid Mechanics. New York: McGraw-Hill, 1974.
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  • 5Furtado M F, da Silva J P P, Multiplicity of solutions for homogeneous elliptic systems with critical growth. J Math Anal Appl, 2012, 385(2): 770-785.
  • 6Ikoma N, Tanaka K. A local mountain pass type result for a system of nonlinear Schrodinger equations. Calc Var, 2011, 40(3/4): 449-480.
  • 7Fang Y Q, Zhang J H. Multiplicity of solutions for elliptic system involving supercritical sobolev exponent. Acta Appl Math, 2011, 115(3): 255 264.
  • 8Figueiredo G M, FFurtado M F. Multiple positive solutions for a quasilinear system of Schrodinger equa- tions. Nonlinear Differ Equ Appl, 2008, 15(3): 309-333.
  • 9Zhang H X, Liu W B. Existence of nontrivial solutions to perturbed p-Laplacian system in involving critical nonlinearity. Boundary Value Problems, 212, 2012:53.
  • 10Alves C O. Multiplicity of positive solutions for a mixed boundary elliptic system. Rocky Mountain J Math, 2008, 38(1): 19-39.

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数学物理学报（A辑）
2013年 第2期

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