含凹凸非线性的p(x)-Laplace方程多正解的存在性(英文)  

Existence of Multiple Positive Solutions for thep(x)-Laplacian Equation with Concave and Convex Nonlinearities

作　　者：熊辉[1] 杨光[2] 

机构地区：[1]东莞理工学院计算机学院,广东东莞523808 [2]东莞理工学院学科建设办公室,广东东莞523808

出　　处：《东莞理工学院学报》2014年第1期1-5,共5页Journal of Dongguan University of Technology

基　　金：Supported by NNSF of China(11271069)~~

摘　　要：研究一个含凹凸非线性的参数型p(x)-7Laplace方程的Dirichlet问题的正解的存在性,在该方程中,超线性项不需要满足Ambrosetti-Rabinowitz条件。利用基于临界点理论的变分方法和Ekeland变分原理,对于取值较小的参数,证明了的所研究的问题至少有两个非平凡的光滑正解。In this paper , a nonlinear parametric Dirichlet problem , driven by the anisotropic p-Laplacian with the combined effects of concave and convex terms , is studied.In this problem, the superlinear nonlinearity needs not satisfy the Ambrosetti-Rabinowitz condition .Using variational methods based on the critical point theory and the Ekeland variational principle , we show that for small values of the parameter , the problem has at least two nontrivial smooth posi-tive solutions.

关 键 词：凹凸非线性 正解存在性 山路原理 EKELAND变分原理 

分 类 号：O175.24[理学—数学] O411.3[理学—基础数学]