Infante, GennaroMascali, GiovanniRodríguez López, Jorge2025-12-192025-12-192024-06-24Gennaro Infante, Giovanni Mascali, Jorge Rodríguez–López, A hybrid Krasnosel’skiĭ-Schauder fixed point theorem for systems, Nonlinear Analysis: Real World Applications, Volume 80, 2024, 104165, ISSN 1468-1218, https://doi.org/10.1016/j.nonrwa.2024.104165https://hdl.handle.net/10347/44609We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel’skiĭ cone compression–expansion type methodologies and Schauder-type ones. In particular we establish a localization of the solution of the system within the product of a conical shell and of a closed convex set. By iterating this procedure we prove the existence of multiple solutions. We illustrate our theoretical results by applying them to the solvability of systems of Hammerstein integral equations. In the case of two specific boundary value problems and with given nonlinearities, we are also able to obtain a numerical solution, consistent with our theoretical resultseng© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article distributed under the terms of the Creative Commons CC-BY licenseAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Fixed point indexFixed point theoremOperator systemHammerstein systemjournal article10.1016/j.nonrwa.2024.1041651878-5719open access