R~N上具有凹凸非线性的半线性椭圆方程

Abstract

RN上具有凹凸非线形的半线性椭圆方程在偏微分方程研究中有着重要的意义.本文利用上下解的方法来研究问题(1)的有界正解存在性,这里:0<p<1<q,a(x)∈L∞loc(RN),N≥3不恒为零.然后研究问题(1)的有界正解存在性与问题-Δu=a(x),x∈RN,N≥3的有界正解存在性的关系.

Semilinear elliptic equation with concave and convex nonlinearities on R~N is important in the research of partial differential equations.In this paper,the question of the existence of bounded and positive solutions for the problem (1) was considered by (using) supur-subsolution method,where 0<p<1<q,a(x)∈L~∞_(loc)(R~N),a(x)≥0,a(x) is not equivalent to zero.Then the relationship of bounded and positive solution between problem (1) and-Δu=a(x),x∈R~N,N≥3 was gained.