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

2025/09/24 by Fernández-Pardo, Laura M., Rodríguez-López, Jorge
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2509.20018

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.

Citations

• Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications
• A fixed point index approach to Krasnosel'skii-Precup fixed point theorem in cones and applications
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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