一类非线性双调和方程在R^N上正整解存在的充分必要条件  

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

作　　者：欧笑杭[1] Xiaohang Ou(Shunde Polytechnic, Guangdong Foshan 528333)

机构地区：[1]顺德职业技术学院

出　　处：《数学物理学报（A辑）》2019年第3期535-544,共10页Acta Mathematica Scientia

摘　　要：研究一类形如△^2u=f(|x|,u,|▽u|)(x∈R^N,N>2)的非线性双调和方程,证明了其在RN上存在正整解的充分必要条件,并给出了解的一些性质.The aim of this paper is to study the nonlinear biharmonic equations of the following form △^2u=f(|x|,u,|▽u|)(x∈R^N,N>2). The Sufficient and necessary condition for the existence of positive entire solutions is proved, and some properties of the solutions are obtained.

关 键 词：非线性双调和方程 正整解 闭凸子集 等度连续 不动点定理 

分 类 号：O175.25[理学—数学]