一类R^n上非线性椭圆型方程正整解的存在性及其性质

The Existence and Properties of Positive Entire Solutions for a Class Nonlinear Elliptic Equations in R^n

以Schauder-Tychonoff不动点定理为工具,应用上、下解得方法,建立一类高维非线性椭圆型方程△_u=f(x,▽u)u~β,(x∈R^n,n≥3,0<β<1)正整解的存在性和性质的定理,所得的结果丰富和发展了Kawano等和许兴业的结果.

Our in this paper aim is to establish the theorems of existence and obain the properties of positive entire solutions a for a class of nonlinear elliptic equations △u=f（x,▽u）uβ,（x∈Rn,n≥3,0〈β〈1） with the Schauder-tychonoff fixed point theorem as the principal tool and the methods of pupersolution and subsolution. It enrichs and develops the results of Kawano et al. and Xu Xingye.