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

2020/04/20 by Reshmi Biswas, Biswas, Reshmi, Sweta Tiwari +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.09451

openalex publication_date 2020/04/20 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28

Abstract

In this article using Nehari manifold method we study the multiplicity of solutions of the following nonlocal elliptic system involving variable exponents and concave-convex nonlinearities: (-Δ)_p(⋅)^s u · amp;=λ~ a(x)| u|^q(x)-2u+(α(x))/(α(x)+β(x))c(x)| u|^α(x)-2u| v| ^β(x),\hspace2mm x∈ Ω;
(-Δ)_p(⋅)^s v · amp;=μ~ b(x)| v|^q(x)-2v+(α(x))/(α(x)+β(x))c(x)| v|^α(x)-2v| u| ^β(x),\hspace2.5mm x∈ Ω;
u=v · amp;=0 ,\hspace1cm x∈ Ω^c:=\mathbb R^N∖Ω, where Ω⊂\mathbb R^N,~N≥2 is a smooth bounded domain, λ,μ>0 are the parameters, s∈(0,1), p∈ C(\mathbb R^N× \mathbb R^N,(1,∞)) and q,α,β∈ C(Ω,(1,∞)) are the variable exponents and a,b,c∈ C(Ω,[0,∞)) are the non-negative weight functions. We show that there exists Λ>0 such that for all λ+μ

Citations

• Fractional p-eigenvalues
• Hitchhikerʼs guide to the fractional Sobolev spaces
• A relation between pointwise convergence of functions and convergence of functionals
• Quasilinear parabolic problem with p(x)-Laplacian: existence,\n uniqueness of weak solutions and stabilization

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