Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities

Date

2020-09-23

Authors

Biswas, Reshmi
Tiwari, Sweta

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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.

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Attribution 4.0 International

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