English

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}
}