R^N上一类奇异半线性调和方程的正整体解

The Positive Entire Solutions of Some Class of Singular Semilinear Harmonic Equations in R^N

本文应用上、下解方法在RN(N≥3)上研究了一类奇异半线性调和方程的正整体解的存在性;同时,为了求其上、下解,以Schauder-Tychonoff不动点定理为工具研究相应方程的径向对称解存在性.

In the paper, an existence theorem of positive entire solution of a class of singular semilinear harmonic equations in RN is established by utilizing supersolution-subsolution method. At the same time, to obtain the disired supersolutions and subsolution, the existence of radially symmetric solutions for the responding equations is also studied by means of Schauder-Tychonoff fixed point theorem.