含极限次临界增长项p-Laplace方程的无穷多解

基金项目: 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(5005930;7005795)

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

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China

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．
- 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
Abstract: A class of p-Laplacian boundary problem on a bounded smooth domain was discussed.The nonlinearity is odd symmetric and limit sub-critical gro wth at infinite.A sequence of critical values of the variational functional was constructed after the generalized Palais-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 subcritical.
- p-Laplacian operator /
- limit sub-critical growth /
- conce ntration-compactness principle /
- Palais-Smale condition /
- asymptotic minimax principle

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