Positive solutions and global bifurcation of strongly coupled elliptic systems

Electronic Journal of Differential Equations

关键词: Elliptic system;    bifurcation;    positive solutions;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this article, we study the existence of positive solutions forthe coupled elliptic systemegin{gather*}-Delta u= lambda (f(u, v)+ h_{1}(x) ) quad ext{in }Omega, \-Delta v= lambda (g(u, v)+ h_{2}(x))quad ext{in }Omega, \u =v=0 quad ext{on }partial Omega,end{gather*}under certain conditions on $f,g$ and allowing $h_1, h_2$ to be singular.We also consider the systemegin{gather*}-Delta u= lambda ( a(x) u + b(x)v+ f_{1}(v)+ f_{2}(u) ) quad ext{in }Ome ga, \-Delta v= lambda ( b(x)u+ c(x)v+ g_{1}(u)+ g_{2}(v) )quad ext{in }Omega , \u =v=0 quad ext{on }partial Omega,end{gather*}and prove a Rabinowitz global bifurcation type theorem to this system.

【 授权许可】

Unknown