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arXiv · 2509.20018

On Krasnosel'skii-Precup fixed point theorem and eigenvalue criteria for existence of positive solutions

Laura M. Fernández-Pardo·Jorge Rodríguez-López
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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.

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Laura M. Fernández-Pardo, Jorge Rodríguez-López. 2025-09-24. On Krasnosel'skii-Precup fixed point theorem and eigenvalue criteria for existence of positive solutions. https://arxiv.org/abs/2509.20018

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