| 含极限次临界增长项p-Laplace方程的无穷多解 |
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| 引用本文： | 耿堤.含极限次临界增长项p-Laplace方程的无穷多解[J].应用数学和力学,2007,28(10):1223-1231. |
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| 作者姓名： | 耿堤 |
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| 作者单位： | 华南师范大学 数学科学学院,广州 510631 |
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| 基金项目： | 国家自然科学基金;广东省自然科学基金 |
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| 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．
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| 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 |
| 文章编号： | 1000-0887（2007）10-1223-09 |
| 收稿时间： | 2006-04-21 |
| 修稿时间： | 2006-04-21 |
Infinitely Many Solutions of p-Laplacian Equations With Limit Sub-Critical Growth |
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| GENG Di.Infinitely Many Solutions of p-Laplacian Equations With Limit Sub-Critical Growth[J].Applied Mathematics and Mechanics,2007,28(10):1223-1231. |
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| Authors: | GENG Di |
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| Institution: | School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China |
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| Abstract: | A class of p-Laplacian boundary problem on a bounded smooth domain was discussed.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 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 sub-critical. |
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| Keywords: | p-Laplacian operator limit sub-critical growth concentration-compactness principle Palais-Smale condition asymptotic minimax principle |
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