Existence and Multiplicity of positive solutions of certain nonlocal scalar field equations

2019/10/17 by Mousomi Bhakta, Bhakta, Mousomi, Souptik Chakraborty +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.07919

openalex publication_date 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study existence and multiplicity of positive solutions of the following class of nonlocal scalar field equations: \\beginaligned (-Δ)^s u + u amp;= a(x) |u|^p-1u+f(x) in ℝ^N, u amp;∈ H^s(ℝ^N) \endaligned . where s ∈ (0,1), N>2s, 1

Cited by

• Mixed local-nonlocal equations with critical nonlinearity on ℝ^N: Non-existence, Existence, and Multiplicity of positive solutions

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