On Krasnosel'skii-Precup fixed point theorem and eigenvalue criteria for existence of positive solutions
Functional Analysis
2025-09-25 v1
Abstract
We provide an alternative approach to Krasnosel'skii-Precup fixed point theorem for operator systems based on the Leray-Schauder fixed point index in cones. Our focus is on the case of operators whose components are entirely of compressive type. The abstract technique is applied to a system of second--order differential equations providing a coexistence positive solution by means of an eigenvalue type criterion.
Keywords
Cite
@article{arxiv.2509.20018,
title = {On Krasnosel'skii-Precup fixed point theorem and eigenvalue criteria for existence of positive solutions},
author = {Laura M. Fernández-Pardo and Jorge Rodríguez-López},
journal= {arXiv preprint arXiv:2509.20018},
year = {2025}
}