P-Laplacian椭圆型方程的整体解

Entire Solutions of P-Laplacian Elliptic Equations

考虑具有边值条件的P-Laplacian椭圆型方程div(▽up-2▽u)=a(x)uγ,x∈Ω解的存在性,其中:p>1,γ>p-1;Ω是Rn上的有界区域;Ω光滑;a(x)是光滑的非负函数。主要证明了在a(x)∈C(Ω-)和a(x)∈C(Rn)两种情况下椭圆型方程解的存在性。

In this paper, we consider the existence of the solutions for the P-Laplacian elliptic equation div（｜u｜p-2u）=a（x）u,x∈Ω to a boundary condition, where P〉1,γ〉p-1;Ω,is a bounded domain with a smooth boundary in R~, and a （x） is nonnegative and smooth. Our main pur-pose is to establish the existence of entire solutions for the elliptic equations, in the case a（x）∈C（Ω）and a（x）∈C（R^n）.