Global bifurcation of positive solutions for a class of superlinear elliptic systems

Ma, Ruyun and Zhu, Yan and Zhang, Yali (2023) Global bifurcation of positive solutions for a class of superlinear elliptic systems. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (36). pp. 1-15. ISSN 1417-3875

Preview

Text p10141.pdf - Published Version Available under License Creative Commons Attribution. Download (598kB) | Preview

Abstract

We are concerned with the global bifurcation of positive solutions for semilinear elliptic systems of the form −∆u =λf(u,v) in Ω, −∆v =λg(u,v) in Ω, u =v=0 on ∂Ω, where λ ∈ R is the bifurcation parameter, Ω ⊂ RN, N ≥ 2 is a bounded domain with smooth boundary ∂Ω. We establish the existence of an unbounded branch of positive solutions, emanating from the origin, which is bounded in positive λ-direction. The nonlinearities f, g ∈ C1(R ×R,(0,∞)) are nondecreasing for each variable and have superlinear growth at infinity. The proof of our main result is based upon bifurcation theory. In addition, as an application for our main result, when f and g subject to the upper growth bound, by a technique of taking superior limit for components, then we may show that the branch must bifurcate from infinity at λ = 0.

Actions (login required)

Edit Item