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- Title
Delay Differential Equations with Differentiable Solution Operators on Open Domains in C((−∞, 0], ℝ<sup>n</sup>) and Processes for Volterra Integro-Differential Equations.
- Authors
Walther, H.-O.
- Abstract
For autonomous delay differential equations x′(t) = f(xt) we construct a continuous semiflow of continuously differentiable solution operators x0 ↦ xt, t ≥ 0, on open subsets of the Fréchet space C((−∞, 0], ℝn). For nonautonomous equations this yields a continuous process of differentiable solution operators. As an application we obtain processes which incorporate all solutions of Volterra integro-differential equations x ′ t = ∫ t 0 k t , s h x s d s .
- Subjects
DELAY differential equations; VOLTERRA equations; AUTONOMOUS differential equations; INTEGRO-differential equations; FRECHET spaces; CONTINUOUS processing
- Publication
Journal of Mathematical Sciences, 2024, Vol 278, Issue 2, p264
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-024-06919-2