R^N中奇异非线性双调和方程存在正整解的充要条件  

Sufficient and Necessary Condition for the Existence of Positive Entire Solutions for Singular Nonlinear Biharmonic Equations on R^N

作　　者：欧笑杭[1] OU Xiaohang(School of Humanities and Social Sciences of Shunde Polytechnic,Shunde,Guangdong,528333,P.R.China)

机构地区：[1]顺德职业技术学院

出　　处：《广东第二师范学院学报》2019年第5期61-69,共9页Journal of Guangdong University of Education

摘　　要：研究一类R^N中形如△^2u=f(|x|,|u|)u^-β,(x∈R^N,N>2,β>0)的奇异非线性双调和方程,建立了3个存在正整解的充分必要条件定理.The aim of this paper is to study the singular nonlinear biharmonic equations of the following form △^2u=f(|x|,| u|)u^-β,(x∈ R ^N,N>2,β>0) in R^N.Three theorems of sufficient and necessary condition for the existence of positive entire solutions are established.

关 键 词：奇异非线性双调和方程 正整解 LEBESGUE控制收敛定理 连续映射 等度连续 不动点定理 

分 类 号：O175.25[理学—数学]