On solution manifolds of some differential equations with more general state-dependent delay
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909102629715968 |
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| author | Walther, Hans-Otto |
| author_facet | Walther, Hans-Otto |
| contents | Differential equations with state-dependent delays define a semiflow of continuously differentiable solution operators in general only on the associated {\it solution manifold} in the Banach space $C^1_n=C^1([-h,0],\mathbb{R}^n)$. For a prototypic example we develop a new proof that its solution manifold is diffeomorphic to an open subset of the subspace given by $ϕ'(0)=0$, without recourse to a restrictive hypothesis about the form of delays which is instrumental in earlier work on the nature of solution manifolds. The new proof uses the framework of algebraic-delay systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On solution manifolds of some differential equations with more general state-dependent delay Walther, Hans-Otto Dynamical Systems Classical Analysis and ODEs 34K43, 34K19, 23K05, 58D25 Differential equations with state-dependent delays define a semiflow of continuously differentiable solution operators in general only on the associated {\it solution manifold} in the Banach space $C^1_n=C^1([-h,0],\mathbb{R}^n)$. For a prototypic example we develop a new proof that its solution manifold is diffeomorphic to an open subset of the subspace given by $ϕ'(0)=0$, without recourse to a restrictive hypothesis about the form of delays which is instrumental in earlier work on the nature of solution manifolds. The new proof uses the framework of algebraic-delay systems. |
| title | On solution manifolds of some differential equations with more general state-dependent delay |
| topic | Dynamical Systems Classical Analysis and ODEs 34K43, 34K19, 23K05, 58D25 |
| url | https://arxiv.org/abs/2402.07636 |