Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities
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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 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.
CitationBiswas, R., & Tiwari, S. (2020). Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities. Electronic Journal of Differential Equations, 2020(98), pp. 1-29.
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