p-Laplacian方程无穷多解的存在性

Existence of Infinitely Many Solutions to p-Laplacian Equation

考虑了一类p-Laplacian方程的D irichlet问题的解.在比(AR)条件更弱的条件下,先证明方程相应的泛函满足(PS)c条件,再应用山路引理得到了该问题无穷多解的存在性.

This paper considers the solutions to the Dirichlet problem in a class of p-Laplacian equation. In the condition weaker than the （AR） condition, the corresponding functional of the equation is first proved satisfying the （PS） c condition. Then, by applying the Mountain Pass Theorem, the existence of infinitely many solutions of the problem is confirmed.