Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916673233092608 |
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| author | Fernández-Pardo, Laura M Rodríguez-López, Jorge |
| author_facet | Fernández-Pardo, Laura M Rodríguez-López, Jorge |
| contents | We present a version of Krasnosel'skii fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index theory in cones, guarantees the existence of a coexistence fixed point - that is, one with nontrivial components. As an application, we prove the existence of periodic solutions with strictly positive components for a system of second-order differential equations. In particular, we address cases involving singular nonlinearities and hybrid terms, characterized by sublinear behavior in one component and superlinear behavior in the other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications Fernández-Pardo, Laura M Rodríguez-López, Jorge Functional Analysis Classical Analysis and ODEs 47H10, 47H11, 34B18, 34B16, 34C25 We present a version of Krasnosel'skii fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index theory in cones, guarantees the existence of a coexistence fixed point - that is, one with nontrivial components. As an application, we prove the existence of periodic solutions with strictly positive components for a system of second-order differential equations. In particular, we address cases involving singular nonlinearities and hybrid terms, characterized by sublinear behavior in one component and superlinear behavior in the other. |
| title | Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications |
| topic | Functional Analysis Classical Analysis and ODEs 47H10, 47H11, 34B18, 34B16, 34C25 |
| url | https://arxiv.org/abs/2504.02774 |