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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 403-412    DOI:
    
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
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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      
Received: 18 September 2016      Published: 01 December 2018
CLC:  O175.25  
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Cite this article:

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.

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


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

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
 
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