A hybrid Krasnosel'skiĭ-Schauder fixed point theorem for systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929368549294080 |
|---|---|
| author | Infante, Gennaro Mascali, Giovanni Rodríguez-López, Jorge |
| author_facet | Infante, Gennaro Mascali, Giovanni Rodríguez-López, Jorge |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06053 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A hybrid Krasnosel'skiĭ-Schauder fixed point theorem for systems Infante, Gennaro Mascali, Giovanni Rodríguez-López, Jorge Classical Analysis and ODEs Functional Analysis Primary 47H10, secondary 45G15, 34B18 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. |
| title | A hybrid Krasnosel'skiĭ-Schauder fixed point theorem for systems |
| topic | Classical Analysis and ODEs Functional Analysis Primary 47H10, secondary 45G15, 34B18 |
| url | https://arxiv.org/abs/2307.06053 |