渐近线性的半线性椭圆方程的解集结构

STRUCTURE OF THE SOLUTION SET OF SEMILINEAR ELLIPTIC EQUATIONS WITH ASYMPTOTIC LINEAR

本文主要讨论一个具体的渐近线性的半线性椭圆方程Δu+λ(u-b)2+ε=0 inΩu=0 onΩu=0 onΩ其解集在λ∈(0,λ1)的情形及在退化点附近解曲线的方向.

In this paper, we mainly discuss the structure of the solution set of semilinear elliptic equations with asymptotic linear as follows：{△u＋λ√（u-b）^2＋ε=0 inΩ u=0 on δΩ when λ∈（0,λ1）and determine the direction of solution curve at a degenerate solution.