含凹凸非线性的p(x)-Laplace方程多正解的存在性  

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

作　　者：熊辉[1] 杨光[1] 

机构地区：[1]东莞理工学院数学教研室,广东东莞523808

出　　处：《江西师范大学学报（自然科学版）》2014年第3期254-257,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11271069)资助项目

摘　　要：利用基于临界点理论的变分方法和Ekeland变分原理,研究含凹凸非线性的参数型p(x)-Laplace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,对于取值较小的参数,证明了所研究的问题至少有2个非平凡的光滑正解.Using variational methods based on the critical point theory and the Ekeland variational principle,a non-linear parametric Dirichlet problem,driven by the anisotropic p（ x）-Laplacian with the combined effects of concave and convex terms,is studied. In this problem,the superlinear nonlinearity does not need to satisfy the Ambrosetti-Rabinowitz condition. It is shown that for small values of the parameter,the problem has at least two nontrivial smooth positive 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]