一类p-Laplacian方程非平凡解的存在性

Existence of Nontrivial Solutions to a Class of p-Laplacian Equation

研究了具有Dirichlet边值问题的p-Laplacian方程-Δ_pu=f(x,u)的非平凡解的存在性。在非线性项f赋予适当的条件下,通过变分法和一些分析技巧,给出了其非平凡解的存在性定理。

This paper was devoted to the p-Laplacian equation -Δpu = f（x,u） with the Dirichlet boundary value.The existence of a nontrivial solution for the p-Laplacian equations under suitable assumptions on the nonlinear term f was proved by using the variational method and some analysis techniques.