A hybrid Krasnosel'skiĭ-Schauder fixed point theorem for systems

2023/07/12 by Gennaro Infante, Infante, Gennaro, Giovanni Mascali +3 · 2 citations
Computer Science · Engineering · #34B18 #Classical Analysis and ODEs (math.CA) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in engineering #Primary 47H10 #Stability and Controllability of Differential Equations #secondary 45G15

paper · pdf · doi:10.48550/arxiv.2307.06053

openalex publication_date 2023/07/12 · openalex created_date 2023/07/14 · openalex updated_date 2026/07/28

Abstract

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\uı 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 results.

Cited by

• Hybrid Nehari-Schauder type fixed point results and applications
• Birkhoff-Kellogg type results in product spaces and their application to differential systems

Related

• A fixed point index approach to Krasnosel'skii-Precup fixed point theorem in cones and applications
• Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity
• On Krasnosel'skii-Precup fixed point theorem and eigenvalue criteria for existence of positive solutions
• Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications
• A Topological and Geometric Approach to Fixed Points Results for Sum of Operators and Applications