Elliptic systems at resonance for jumping non-linearities
Date
2016-03-15
Authors
Lakhal, Hakim
Khodja, Brahim
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the existence of nontrivial solutions for the problem
-Δu = α1u+ - β1u‾ + ƒ(x, u, v) + h1(x) in Ω,
-Δv = α2v+ - β2v‾ + g(x, u, v) + h2(x) in Ω,
u = v = 0 on ∂Ω,
where Ω is a bounded domain in ℝN, and h1, h2 ∈ L2(Ω). Here [αj, βj] ∩ σ(-∆) = λ, where σ(∙) is the spectrum. We use the Leray-schauder degree theory.
Description
Keywords
Topological degree, Elliptic systems, Homotopy
Citation
Lakhal, H., & Khodja, B. (2016). Elliptic systems at resonance for jumping non-linearities. Electronic Journal of Differential Equations, 2016(70), pp. 1-13.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.