带形区域上半线性椭圆方程的L^p分歧问题

BIFURCATION IN L^P(Ω) FOR SEMILINEAR ELLIPTIC EQUATION IN STRIP-LIKE DOMAINS

本文证明了带形区域Ω上的半线性椭圆型方程λ△u(z)+u(z)=f(z,u),u(z)∈H_0~1(Ω),λ<0 (*)非平凡解的存在性及L^p分歧结果:当p∈[1,+∞)时,(0,0)为方程(*)在L′(Ω)中的分歧解;当p=+∞时,方程(*)在O处不发生L′分歧现象。

In this paper, we consider the existence of nontrival solution and bifurcation in L'(Ω) for the semilinear elliptic equation λ△u(z)+u(z)=f(z,u),u(z)∈H_0~1(Ω),λ<0, (*) where Ω is a strip-like domain. We prove that (0, 0) is a bifurcation solution of (*) in L'(Ω) if p∈[1,+∞), and that (0, 0) is not a bifurcation solution of (*) in L'(Ω) if p