带梯度项的半线性椭圆型方程正径向整大解的存在性

The Existence of Entire Large Positive Radial Solutions for Semilinear Elliptic Equation with Gradient Term

本文研究带梯度项的半线性椭圆型方程正径向整大解的存在性。先利用Banach不动点定理和反证法得出正径向解的局部及整体存在性,进而得到正径向整大解的存在性结论。结果发现,正径向整大解的存在性依赖于梯度项的系数符号和指数的范围。

The existence of entire large positive radial solutions for semilinear elliptic equation was invesrigated. The existence of local and global positive radial solutions was proved by using Banach fixed point theorem and reductio absurdum thus and the existence result of entire large positive radial solutions was obtained. It was fauued that the existence of entire large positive radial solutions depends on the sign of the coefficient for gradient term and the range of exponent.