一类高维非线性椭圆型方程正整解的存在性

The Existence of Positive Entire Solutions for a Class of Higher Dimensions Nonlinear Elliptic Equations

以Shauder-Tychonoff不动点定理为工具,建立一类高维非线性椭圆型方程Δu=f(x,Δu)uγ(x∈Rn,n≥3,0<γ<1)正的整体解的存在性定理,并给出了解的有关性质.

In this paper, our aim is to establish the theorems of existence of positive entire solutions for a class of higher dimensions nonlinear elliptic equations △u= f（x, △↓u） u^y （x ∈ R^n, n=3,0〈y〈1） with the Schauder-tychonoff fixed point theorem as the principal and the related properties of the solutions were obtained.