Positive Solutions and Global Bifurcation of Strongly Coupled Elliptic Systems
نویسنده
چکیده
In this article, we study the existence of positive solutions for the coupled elliptic system −∆u = λ(f(u, v) + h1(x)) in Ω, −∆v = 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 −∆u = λ(a(x)u+ b(x)v + f1(v) + f2(u)) in Ω, −∆v = 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.
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