R^N上具有凹凸非线性的半线性椭圆方程  

Semilinear Elliptic Equation with Concave and Convex Nonlinearities on R^N

作　　者：王培林[1] 谭忠[2] 

机构地区：[1]福建农林大学计算机与信息学院,福建福州350002 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2005年第3期311-312,共2页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10171083);福建农林大学青年教师基金(2001 91)资助

摘　　要：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.

关 键 词：半线性椭圆方程 R^N 非线性 正解存在性 偏微分方程 有界 上下解 非线形 

分 类 号：O175.25[理学—数学] O174.13[理学—基础数学]