摘要
考虑椭圆型方程Δu+f(X,u)=0在RN,N≥3上的全局正解,其中u→f(x,u)在u=0未假定是正则的,且f(x,u)可能更广泛而同时包含下线性项和奇异项。借助于阐方法和常微分方程研究,给出若干充分条件以保证全局正解的存在性,且这些正解可在无穷远处趋于任意预定的充分大常数。
In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.
关键词
奇异半线性椭圆型方程
有界全局正解
闸方法
singular semilinear elliptic equation, bounded positive entire solution, barrier method