一类非线性多重调和方程△mu=f(|x|,u,|▽u|)的正整解

The Positive Entire Solutions of a Class of Nonlinear Multiple Harmonic Equations △mu=f(|x|,u,|▽u|)

中文关键词:  多重调和方程  正整解  闭凸子集  相对紧  不动点定理.

英文关键词:multiple harmonic equation  positive entire solutionl close convex subest  relative compactness  fixed point theorem.

中文摘要:

      本文建立了一类Rⁿ(n≥3)中非线性多重调和方程△^mu=f(|x|,u,|▽u|)(m≥2)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,推广了文[1]-[4]的有关结果.

英文摘要:

      In this paper, we establish the theorems of existence of positive radially symmtry entire solutions for a class of nonlinear multiple harmonic equations △^mu=f(|x|,u,|▽u|) (m≥2) on Rⁿ(n≥3) and present the properties of the solutions. The results of this paper may be regarded as an extension of [1]-[4].