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

  1. Rodríguez-López, Jorge 1
  1. 1 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

Zeitschrift:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Datum der Publikation: 2021

Ausgabe: 20

Nummer: 3

Art: Artikel

DOI: 10.1007/S12346-021-00505-6 DIALNET GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: Qualitative theory of dynamical systems

Ziele für nachhaltige Entwicklung

Zusammenfassung

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.

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