Hybrid and Component-wise Leggett-Williams type Fixed Point Theorems in Product Spaces with Applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911703447371776 |
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| author | Fernández-Pardo, Laura María |
| author_facet | Fernández-Pardo, Laura María |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hybrid and Component-wise Leggett-Williams type Fixed Point Theorems in Product Spaces with Applications Fernández-Pardo, Laura María Functional Analysis Classical Analysis and ODEs 47H10, 47H11, 45G15, 34B18 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. |
| title | Hybrid and Component-wise Leggett-Williams type Fixed Point Theorems in Product Spaces with Applications |
| topic | Functional Analysis Classical Analysis and ODEs 47H10, 47H11, 45G15, 34B18 |
| url | https://arxiv.org/abs/2605.21732 |