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 Singularity on R^n

作　　者：许兴业[1] 

机构地区：[1]广东教育学院数学系,广州510310

出　　处：《数学物理学报（A辑）》2009年第1期87-93,共7页Acta Mathematica Scientia

基　　金：广东省高校自然科学研究基金(Z02082)资助

摘　　要：该文以Schauder-Tychonoff不动点定理为工具,建立了一类R^n上带奇异性的非线性双调和方程△~2u=f(|x|,u,|▽u|)u^(-β)(x∈R^n,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献[1-5]的结果.In this paper, author＇s aim is to establish the theorems of existence of positive radially symmetric entire solutions for a class of singular nonlinear biharmonic equation △^2u = f（｜x｜, u, ｜↓△u｜）u^-β（x ∈ R^n, n ≥ 3, β 〉 0） on Rn with the Schauder-tychonoff fixed point theorem as the principal tool, and presents the properties of the solutions. They enrich and develop the theory and application of papes [1-5].

关 键 词：双调和方程 正整解 LEBESGUE控制收敛定理 等度连续 不动点定理. 

分 类 号：O175.25[理学—数学]