On a nonlinear parametric Robin problem with a locally defined reaction. (August 2019)

• Record Type: Journal Article
• Authors: Gasiński, Leszek; Papageorgiou, Nikolaos S.
• Is Part Of: Nonlinear analysis. Volume 185(2019)
• Page Start: 374
• Page End: 387
• Publication Date: 2019-08
• Subjects: 35J20 -- 35J60 -- 58E05; Reaction locally defined -- Nonlinear regularity -- Extremal constant sign solution -- 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.2019.03.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a nonlinear nonhomogeneous Robin problem with a parametric potential term and a Carathéodory reaction which is only locally defined. We show that for all values of the parameter in an upper half line, the equation has at least three nontrivial smooth solutions, two of constant sign and the third nodal. Under a symmetry condition on the reaction, we show the existence of a sequence of nodal solutions converging to zero in C 1 ( Ω ¯ ) .