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

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.