R^N上半线性椭圆方程的正整体解

Positive Entire Solutions of Semilinear Elliptic Equations in R^N

设f:RN×R+×RN→R为连续函数.本文研究形如?u+f(x,u,?u)=0,x∈RN(N≥3)的半线性椭圆方程的非径向正整体解,给出了该类方程存在衰减(即当x→∞时趋于0)的正整体解的充分条件.

Suppose f：R^N×Rb×R^N→R is a continuous function. This paper investigates N-dimensional semilinear elliptic equations of the form △μ＋f（x,u,Δ↓u）=0,x∈R^N/（N≥3） and gives a sufficient condition under which the equations have a positive entire solution vanishing at infinity.