一类奇异非线性多重调和方程存在正整解的充分必要条件  

Sufficient and necessary condition for the existence of positive entire solutions of a class of singular nonlinear polyharmonic equations

作　　者：许兴业 XU Xing-ye(Department of Public Course Teaching, South China Business College,Guangdong University of Foreign Studies, Guangzhou 510545, China)

机构地区：[1]广东外语外贸大学南国商学院公共课教学部,广东广州510545

出　　处：《高校应用数学学报（A辑）》2017年第4期403-412,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：广东外语外贸大学南国商学院校级科研重点课题(16-005A)

摘　　要：研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u^(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.In this paper,the aim is to study the singular nonlinear polyharmonic equations of the following form￠mu=f(jxj;u;jruj)u?ˉ.The su±cient and necessary condition for the existence of positive radial symmetric entire solutions is proved,and some properties of the solutions are obtained.

关 键 词：非线性多重调和方程 LEBESGUE控制收敛定理 等度连续 相对紧 不动点定理 

分 类 号：O175.25[理学—数学]