A positive eigenvalue result for semilinear differential equations in Banach spaces with functional initial conditions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917175184326656 |
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| author | Infante, Gennaro Rubbioni, Paola |
| author_facet | Infante, Gennaro Rubbioni, Paola |
| contents | We study the existence of positive eigenvalues with associated nonnegative mild eigenfunctions for a class of abstract initial value problems in Banach spaces with functional, possibly nonlocal, initial conditions. The framework includes periodic, multipoint, and integral average conditions. Our approach relies on nonlinear analysis, topological methods, and the theory of strongly continuous semigroups, yielding results applicable to a wide range of models. As an illustration, we apply the abstract theory to a reaction-diffusion equation with a nonlocal initial condition arising from a heat flow problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A positive eigenvalue result for semilinear differential equations in Banach spaces with functional initial conditions Infante, Gennaro Rubbioni, Paola Classical Analysis and ODEs Analysis of PDEs 34B10, 34B18, 34G20, 35K57 We study the existence of positive eigenvalues with associated nonnegative mild eigenfunctions for a class of abstract initial value problems in Banach spaces with functional, possibly nonlocal, initial conditions. The framework includes periodic, multipoint, and integral average conditions. Our approach relies on nonlinear analysis, topological methods, and the theory of strongly continuous semigroups, yielding results applicable to a wide range of models. As an illustration, we apply the abstract theory to a reaction-diffusion equation with a nonlocal initial condition arising from a heat flow problem. |
| title | A positive eigenvalue result for semilinear differential equations in Banach spaces with functional initial conditions |
| topic | Classical Analysis and ODEs Analysis of PDEs 34B10, 34B18, 34G20, 35K57 |
| url | https://arxiv.org/abs/2512.23876 |