R^n上一类椭圆方程的多解性

On the entire solutions for a class of semilinear elliptic equations in R^n

考虑一类半线性椭圆方程的整体解 .首先给出此方程的径向解 ,并以它及上下解为主要工具证明了在不同条件下方程存在正整体解 .主要结果是 :当方程的非线性项满足不同条件时 ,方程存在无穷多个指数增长解与衰退解 .

The existence of positive entire solutions for a class of semilinear elliptic equations in Rn is discussed. By its lower and upper solutions as the main methods, the existence of the entire solutions of equations is proven under distinct conditions. The main result is that the equation has an infinite number of exponent increasing solutions and decaying solutions when its nonlinear term satisfies different conditions.