类p-双调和方程Dirichlet问题无穷多解的存在性

详细信息

Infinitely Many Solutions for p-Biharmonic-like Equations Involving the Dirichlet Problem

摘要: 讨论了 ${\bf R}^N$ 中有界光滑区域上的一类类 $p-$ 双调和方程的无穷多解问题, 其中 $2pN$ , 非线性项不必具有奇对称性. 利用Ricceri的一个变分原理, 得到了无穷多解的存在性, 进而证明了当非线性项在零点(无穷远点)振荡时, 无穷多解按范数趋于零(趋于无穷)
- 类p-双调和算子 /
- Ricceri变分原理 /
- 无穷多解
Abstract: The aim of this paper is to discuss the infinitely many solutions of a class of $p$ -biharmonic-like equations on a bounded smooth domain of ${\bf R}^N$ ,where $2pN$ , and the nonlinearity may not be odd symmetric. Using a recent variational principle of Ricceri, some results of existence of infinitely many solutions are shown, the norms of those solutions tend to zero (to infinity) whenever the nonlinearity oscillates at zero (at infinity).
- p-Biharmonic-like operators /
- Ricceri variational principle /
- Infinitely many solutions