带有一般非线性项的一类p拉普拉斯型方程基态解的存在性

Existence of Ground State Solutions for the Class of P-laplacian Type Equation with the General Nonlinearity

研究p拉普拉斯型非线性椭圆方程:{Δ_pu+|u|^(p-2)u=f(u)于R^N,u∈W^(1,p)(R^N),p≥2.其中非线性项f∈C并且满足类似于文献[1]的非线性项条件。我们无须借助于Nehari流形即证明了上述方程的基态解的存在性。证明的方式主要是基于变分方法。本文的结果是文献[1]中的半线性椭圆方程的结果在p拉普拉斯型方程中的推广。

In this paper, we study the following p-Laplacian type equation:{Δ_pu+|u|^(p-2)u=f(u)in R^N,u∈W^(1,p)(R^N),p≥2,,where f ∈ C and satisfies the conditions of [1].In this paper, we get the existence of ground state solutions of the above equation. Our result can be seen as an extension of [1] for semilinear elliptic equations to the p-Laplacian type problem.