Component-wise Krasnosel’skii type fixed point theorem in product spaces and applications

We present a version of Krasnosel’skiĭ fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index theory in cones, guarantees the existence of a coexistence fi...

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Detalles Bibliográficos
Autores: Rodríguez López, Jorge, Fernández-Pardo, Laura M.
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/43742
Acceso en línea:https://hdl.handle.net/10347/43742
Access Level:acceso abierto
Palabra clave:Coexistence fixed point
Fixed point index
Positive solution
Nonlinear systems
Periodic solution
Descripción
Sumario:We present a version of Krasnosel’skiĭ fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index theory in cones, guarantees the existence of a coexistence fixed point, that is, one with nontrivial components. As an application, we prove the existence of periodic solutions with strictly positive components for a system of second-order differential equations. In particular, we address cases involving singular nonlinearities and hybrid terms, characterized by sublinear behavior in one component and superlinear behavior in the other.