R^n上带奇异性的非线性双调和方程的正整解

The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singular on R^n

以Schauder-Tychonoff不动点定理为工具,建立了一类Rn上带奇异性的非线性双调和方程Δ2u=f(|x|,u,|▽u|)u-β(n≥3,β>0)正的径向对称整体解的存在性定理,并给出了解的有关性质,所得的结果丰富和发展了文[1-4]的结果.

Author＇s aim is to establish the theorems of existence of positive radially symmetric entire solutions for a class singular nonlinear biharmonic△^2u=f（f｜x｜,u,｜△↓u｜）u^-β（n≥3,β〉0） on R^n with the Schauder-tychonoff fixed point theorem as the principal, and present about the properties of the solutions. It enriehs and develops the theory and apply of paper [1]--[4].