含极限次临界增长项p-Laplace方程的无穷多解  

Infinitely Many Solutions of p-Laplacian Equations With Limit Sub-Critical Growth

作　　者：耿堤[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《应用数学和力学》2007年第10期1223-1231,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10371045);广东省自然科学基金资助项目(50059307005795)

摘　　要：讨论了有界光滑区域上一类p-Laplace方程,非线性项具奇对称性且在无穷远为极限次临界增长.证明了变分泛函在大范围内满足推广的Palais-Smale条件,构造了变分泛函的一列临界值,进而得到了无穷多个弱解的存在性,对应泛函的能量趋于正无穷.所得到的结果推广了次临界增长的情形.A class of p-Laplacian boundary problem on a bounded smooth domain was disussed. The nonlinearity is odd symmetric and limit sub-critical growth at infinite. A sequence of critical values of the variational functional was constructed after the generalized Palai-Smale condition was verified. It is obtained that the problem possesses infinitely many solutions and corresponding energy levels of the functional pass to positive infinite. The result is a generalization of the similar problem in case of sub- critical.

关 键 词：P-LAPLACE算子 极限次临界增长 集中紧性原理 广义的Palais—Smale条件 渐近极小极大值原理 

分 类 号：O175.25[理学—数学]