Positive solutions and global bifurcation of strongly coupled elliptic systems

In this article, we study the existence of positive solutions for the coupled elliptic system -Δu = λ (f(u; v) + h1(x)) in Ω -Δv = λ (g(u; v) + h2(x)) in Ω u = v = 0 on ∂Ω; under certain conditions on f; g and allowing h1; h2 to be singular. We also consider the system -Δu = λ (a(x)u + b(x)v + f1(v) + f2(u)) in Ω -Δu = λ (b(x)u + c(x)v + g1(u) + g2(v)) in Ω; u = v = 0 on ∂Ω; and prove a Rabinowitz global bifurcation type theorem to this system. ©2013 Texas State University - San Marcos.