Nonlinear Robin problems with indefinite potential. (June 2020)

• Record Type: Journal Article
• Authors: Leonardi, S.; Onete, Florin I.
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: primary 35J20 35J60 -- secondary 58E05; Nonlinear regularity -- Nonlinear maximum principle -- Extremal constant sign solutions -- Nodal solutions -- Critical groups; 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.2020.111760
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a nonlinear Robin problem driven by the p -Laplacian plus an indefinite potential. The conditions on the source term are minimal. We prove two multiplicity theorems with sign information for all the solutions. In the semilinear case ( p = 2 ), we show that we can have multiple nodal solutions. We apply our results to a special class of logistic equations with equidiffusive reaction.