A hybrid Krasnosel'skiĭ-Schauder fixed point theorem for systems
We 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 pr...
| Authors: | ; ; |
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| Format: | Article |
| Publication date: | 2024 |
| Country: | España |
| Institution: | Universidad de Santiago de Compostela (USC) |
| Repository: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Language: | English |
| OAI Identifier: | oai:minerva.usc.gal:10347/44609 |
| Online Access: | https://hdl.handle.net/10347/44609 |
| Access Level: | Open access |
| Keyword: | Fixed point index Fixed point theorem Operator system Hammerstein system |
| Summary: | We 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 results |
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