Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. (April 2015)

• Record Type: Journal Article
• Authors: Maia, Liliane A.; Montefusco, Eugenio; Pellacci, Benedetta
• Is Part Of: Nonlinear analysis. Volume 116(2015)
• Page Start: 193
• Page End: 209
• Publication Date: 2015-04
• Subjects: 35J61 -- 35Q51 -- 35Q55; Schrödinger equations -- Saturable media -- Concentration phenomena -- Singularly perturbed elliptic equation -- Asymptotically linear nonlinearities -- Penalization 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.2014.09.030
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given.