Existence of solutions for a nonhomogeneous semilinear elliptic equation. (June 2020)

• Record Type: Journal Article
• Authors: Arcoya, David; de Paiva, Francisco Odair; Mendoza, José M.
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J20 -- 35J61 -- 58E05; Semilinear elliptic problem -- Variational methods -- Existence of solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111728
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For a bounded domain Ω, a bounded Carathéodory function g in Ω × R, p > 1 and a nonnegative locally integrable function h in Ω which is strictly positive in a set of positive measure we prove that, contrarily with the case h ≡ 0, there exists a solution of the semilinear elliptic problem − Δ u = λ u + g ( x, u ) − h | u | p − 1 u + f, in Ω u = 0, on ∂ Ω, for every λ ∈ R and f ∈ L 2 ( Ω ) .