A sub-supersolution approach for Neumann boundary value problems with gradient dependence. (August 2020)

• Record Type: Journal Article
• Authors: Motreanu, Dumitru; Sciammetta, Angela; Tornatore, Elisabetta
• Is Part Of: Nonlinear analysis. Volume 54(2020)
• Publication Date: 2020-08
• Subjects: Quasilinear elliptic equation -- Neumann problem -- Gradient dependence -- Sub-supersolution -- Positive solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103096
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Existence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems.