Mixed local-nonlocal quasilinear problems with critical nonlinearities

2023/08/14 by João Vítor da Silva, da Silva, João Vitor, Alessio Fiscella +3 · 6 citations
Computer Science · Mathematics · #35A16 #35B33 #35J92 #35M12 #35P30 35A15 #35R11 #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.2308.07460

openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study existence and multiplicity of nontrivial solutions of the following problem \ -Δ_p u+(-Δ_p)^s u · amp; = · amp; λ|u|^q-2u+|u|^p^∗-2u · amp; in Ω,
u · amp; = · amp; 0 · amp; on ℝ^N ∖ Ω, . where Ω⊂ ℝ^N is a bounded open set with smooth boundary, dimension N≥ 2, parameter λ>0, exponents 0

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