A mixed local and nonlocal supercritical Dirichlet problems

2023/03/06 by D. S. Amundsen, Amundsen, David, Abbas Moameni +3
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.2303.03273

openalex publication_date 2023/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we consider a mixed local and nonlocal Dirichlet problem with supercritical nonlinearity. We first establish a multiplicity result for the problem Lu=|u|^p-2u+μ|u|^q-2u~~in~~Ω,~~~~~ u=0~~in~~ℝ^N∖Ω,~~~ (0.1) where L=-Δ+(-Δ)^s for s∈(0,1) and Ω⊂ℝ^N is a bounded domain. Precisely, we show that problem (0.1) for 1

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