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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (4): 403-412    
    
一类奇异非线性多重调和方程存在正整解的充分必要条件
许兴业
广东外语外贸大学南国商学院公共课教学部, 广东广州510545
Suffcient and necessary condition for the existence of positive entire solutions of a class of singular nonlinear polyharmonic equations#br#
XU Xing-ye
Department of Public Course Teaching, South China Business College, Guangdong University of Foreign Studies, Guangzhou 510545, China
 全文: PDF 
摘要： 研究一类奇异非线性多重调和方程$\Delta^{m}u=f(|x|,u, |\nabla u|)u^{-\beta}$ , 给出了方程存在正的径向对称整体解的充分必要条件和解的性质.
关键词： 非线性多重调和方程;  Lebesgue控制收敛定理;  等度连续;  相对紧;  不动点定理
    
Abstract: In this paper, the aim is to study the singular nonlinear polyharmonic equations
of the following form $\Delta^{m}u=f(|x|,u, |\nabla u|)u^{-\beta}$. The su±cient and necessary condition for the
existence of positive radial symmetric entire solutions is proved, and some properties of the
solutions are obtained.
Key words: nonlinear polyharmonic equation    Lebesgue dominated convergence theorem    equicontinuity    relative compactness    fixed point theorem
收稿日期: 2016-09-18 出版日期: 2018-12-01
CLC:  O175.25  
基金资助: 广东外语外贸大学南国商学院校级科研重点课题(16-005A)
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引用本文:

许兴业. 一类奇异非线性多重调和方程存在正整解的充分必要条件[J]. 高校应用数学学报, 2017, 32(4): 403-412.

XU Xing-ye. Suffcient and necessary condition for the existence of positive entire solutions of a class of singular nonlinear polyharmonic equations#br#. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 403-412.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I4/403

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