Fixed point index theory for decomposable multivalued maps and applications to discontinuous ϕ-Laplacian problems. (October 2020)

• Record Type: Journal Article
• Authors: Precup, Radu; Rodríguez-López, Jorge
• Is Part Of: Nonlinear analysis. Volume 199(2020)
• Publication Date: 2020-10
• Subjects: 47H11 -- 47H10 -- 34A36 -- 34A60; Fixed point index theory -- Discontinuous differential equation -- Multiple solutions -- ϕ-Laplacian equation -- Lower and upper solutions; 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.2020.111958
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we develop a fixed point index theory for decomposable multivalued maps, that is, compositions of two multivalued nonlinear upper semicontinuous maps. As an application, this fixed point index theory is combined with the method of lower and upper solutions in order to obtain new existence, localization and multiplicity results for ϕ -Laplacian problems with discontinuous nonlinearities and nonlinear functional boundary conditions.