Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities
Date
2020-09-23
Authors
Biswas, Reshmi
Tiwari, Sweta
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, using Nehari manifold method we study the multiplicity of solutions of the nonlocal elliptic system involving variable exponents and concave-convex nonlinearities,
(-∆)sp(∙)u = λα(x)|u|q(x)-2u + α(x)/α(x) + β(x) c(x)|u|α(x)-2 u|v|β(x), x ∈ Ω<;
(-∆)sp(∙)v = μb(x)|v|q(x)-2v + α(x)/α(x) + β(x) c(x)|v|α(x)-2</sup> v|u|β(x), x ∈ Ω;
u = v = 0, x ∈ Ωc := ℝN \ Ω,
where Ω ⊂ ℝN, N ≥ 2 is a smooth bounded domain, λ, μ > 0 are parameters, and s ∈ (0, 1). We show that there exists Λ > 0 such that for all λ + μ < Λ, this system admits at least two non-trivial and non-negative solutions under some assumptions on q, α, β, α, b, c.
Description
Keywords
Nonlocal problem with variable exponents, Elliptic system, Nehari manifold, Fibering map, Concave-convex nonlinearities
Citation
Biswas, R., & Tiwari, S. (2020). Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities. <i>Electronic Journal of Differential Equations, 2020</i>(98), pp. 1-29.
Rights
Attribution 4.0 International