Compression–Expansion Fixed Point Theorems for Decomposable Maps and Applications to Discontinuous ϕ-Laplacian problems

• Published in: Qualitative theory of dynamical systems Vol. 20; no. 3
• Main Author: Rodríguez–López, Jorge
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.11.2021; Springer Nature B.V
• Subjects: Boundary conditions; Cones; Decomposition; Difference and Functional Equations; Differential equations; Dynamical Systems and Ergodic Theory; Fixed points (mathematics); Mathematics; Mathematics and Statistics; Nonlinearity; Theorems; Discontinuous differential equation; 47H10; 34A36; Compression–expansion fixed point theorem; Laplacian equation; Positive solution; Differential inclusion; 34A60; 47H04
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-021-00505-6

In this paper, we prove new compression–expansion type fixed point theorems in cones for the so-called decomposable maps, that is, compositions of two upper semicontinuous multivalued maps. As an application, we obtain existence and localization of positive solutions for a differential equation with...