On a resonant elliptic problem with singular terms. (June 2020)

• Record Type: Journal Article
• Authors: Anello, Giovanni; Faraci, Francesca
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J20; Resonant elliptic problem -- Singular terms -- Indefinite nonlinearities -- Variational methods; 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.2020.111818
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In the present paper we consider the singular resonant elliptic problem ( P μ ) − Δ u = λ 1 u + ( u s − 1 − μ u r − 1 ) χ { u > 0 }, in Ω u ≥ 0 in Ω u = 0, on ∂ Ω and prove the existence of a non trivial solution in the cases 0 < r < s < 1 and 0 < s < r < 1 .