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

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...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 20; no. 3
Main Author Rodríguez–López, Jorge
Format Journal Article
LanguageEnglish
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
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Summary: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 ϕ -Laplacian and discontinuous nonlinearity subject to multi-point boundary conditions. As far as we are aware, the existence results are new even in the classical case of continuous nonlinearities.
Bibliography:ObjectType-Article-1
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ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-021-00505-6