Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight. (July 2020)

• Record Type: Journal Article
• Authors: Boscaggin, Alberto; Feltrin, Guglielmo
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 34B08 -- 34B18 -- 35B09 -- 47H11; Minkowski-curvature operator -- Indefinite weight -- Neumann problem -- Positive solutions -- Radial solutions -- Topological degree; 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.2020.111807
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem div ( ∇ u 1 − | ∇ u | 2 ) + λ a ( | x | ) u p = 0, in B, ∂ ν u = 0, on ∂ B, where B is a ball centered at the origin, a ( | x | ) is a radial sign-changing function with ∫ B a ( | x | ) d x < 0, p > 1 and λ > 0 is a large parameter. The proof is based on the Leray–Schauder degree theory and extends to a larger class of nonlinearities.