Existence and multiple of solutions for a class integro-differential equations with singular term via variational and Galerkin methods. (February 2023)

• Record Type: Journal Article
• Authors: dos Santos, Gelson C.G.; de Assis Lima, Natan; de Lima, Romildo N.
• Is Part Of: Nonlinear analysis. Volume 69(2023)
• Publication Date: 2023-02
• Subjects: Nonlocal problems -- Variational methods -- Integral operators -- Galerkin method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103752
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we focus our attention on the singular and nonlocal equation ( P ) − d i v ( a ( x ) ∇ u ) + η ψ ( x ) ∫ Ω φ u = λ ( u + ) α + ( u + ) p in Ω, u = 0 on ∂ Ω, for which we prove the existence of solutions. Here Ω ⊂ R N is a bounded smooth domain, u + = max { u, 0 }, η ∈ R, λ > 0, α ∈ ( 0, 1 ), p ∈ ( 0, 2 ∗ ) and a, ψ, φ are functions whose properties will be timely introduced.