Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications
Functional Analysis
2025-04-04 v1 Classical Analysis and ODEs
Abstract
We present a version of Krasnosel'skii 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.
Keywords
Cite
@article{arxiv.2504.02774,
title = {Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications},
author = {Laura M Fernández-Pardo and Jorge Rodríguez-López},
journal= {arXiv preprint arXiv:2504.02774},
year = {2025}
}