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R^N中一类拟线性椭圆方程组非负解的存在性和多重性 被引量：3

Existence and Multiplicity of Nonnegative Solutions for a Quasilinear System in R^N
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摘要 利用极小极大原理和Ljusternik-Schnirelmann畴数理论,研究了R^N中一类拟线性椭圆方程组.当2≤p,q<N时,α≥0,β≥0满足α+β+2>max{p,q}和(α+1)/p~*+(β+1)/q~*≤1,通过建立解的个数与正连续函数V和W达到极小值集合的拓扑量之间的关系,得到拟线性方程组至少存在cat_(M_δ)(M)个不同的非负解. In this paper,we consider a class of quasilinear elliptic equations in R^N by the minimax theorems and the Ljusternik-Schnirelmann theory.When 2≤p,qN,α≥0 andβ≥0 satisfy the conditions ofα＋β＋2max{p,q} and（a＋1）/（p~＊）＋（β＋1）/（q~＊）≤1,the quasilinear system has at least cat_M_δ（M） nonnegative solutions by relating the number of solutions with the topology of the set where V and W attain its minimum.
作者 张文丽 钟立楠
机构地区 长治学院数学系山西 延边大学理学院数学系
出处 《数学物理学报（A辑）》 CSCD 北大核心 2013年第1期174-184,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(10771105) 山西省高校科技研究开发项目(20111129)资助
关键词 拟线性方程组 NEHARI流形 极小极大原理 Ljusternik-Schnirelmann畴数理论 Quasilinear system Nehari manifold Minimax theorems Ljusternik-Schnirelmanntheory.
分类号 O175 [理学—基础数学]
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参考文献18

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共引文献1

同被引文献41

  • 1Astrita G, Marrucci G. Principles of Non-Newtonian Fluid Mechanics. New York: McGraw-Hill, 1974.
  • 2Martinson L K, Pavlov K B. Unsteady shear flows of a conducting fluid with a rheological power law. Magnitnaya Gidrodinamika, 1971, 7(2): 50-58.
  • 3Figueiredo G M. Multiplicity of solutions for a class of elliptic systems in IN. Electronic Journal of Differential Equations, 2006, 76:1-12.
  • 4Alves C O. Local mountain pass for a class of elliptic system. J Math Anal Appl, 2007, 335(1): 135-150.
  • 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.

引证文献3

二级引证文献1

数学物理学报（A辑）
2013年 第1期

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