摘要
本文以关于非线性全连续算子的锥不动点定理为工具，研究半线性椭圆边值问题上Δu+λa(|x|)u+f(|x|,u)=0(x∈Ω)，u|=0及Δu+λf(|x|,u)=0(x∈Ω)，u|=0．在不假定f单调的情况下，本文得出了上述问题存在正径向解的若干充分条件．
In this paper,by means of cone fixed point theorem for nonlinear completely continuous operator，we study the semilinear elliptic boundary value problemsΔ+λa(|x|)u+f(|x|,u)=0(x∈Ω，u| =0 and Δu＋λf(|x|，u)=0(x∈Ω，u|=0，where Ω=｛x∈R^N：0＜r_1 ＜|x|＜ r_2｝,N≥ 2.Under the case without assumptions of monotoniciy for f,several sufficient conditions for the existence of positive radial solutions of the above problems are obtained．
出处
《应用数学》
CSCD
1998年第1期29-33,共5页
Mathematica Applicata
基金
国家自然科学基金
关键词
半线性
特征值
正径向解
椭圆型方程
Semilinear elliptic equation,Eigenvalue,Positive radial solution,Cone fixed point theorem
