Hybrid and Component-wise Leggett-Williams type Fixed Point Theorems in Product Spaces with Applications
Functional Analysis
2026-05-22 v1 Classical Analysis and ODEs
Abstract
In this paper, we present new multiplicity fixed point theorems for operators acting on Cartesian products of two normed linear spaces. We show that Leggett-Williams type conditions in each component of the system guarantee the existence of nine distinct fixed points, of which four of them are coexistence fixed points, i.e., points with all components nontrivial. In addition, a hybrid approach combining Leggett-Williams conditions in one component with Krasnosel'skii compression-expansion conditions in the other allows us to obtain three fixed points. As an application, we establish the existence of multiple positive solutions for nonlinear systems of second-order equations with two-point boundary conditions.
Keywords
Cite
@article{arxiv.2605.21732,
title = {Hybrid and Component-wise Leggett-Williams type Fixed Point Theorems in Product Spaces with Applications},
author = {Laura María Fernández-Pardo},
journal= {arXiv preprint arXiv:2605.21732},
year = {2026}
}