A Class of Linear Partial Neutral Functional Differential Equations with Nondense Domain

✍ Scribed by Mostafa Adimy; Khalil Ezzinbi

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 498 KB
• Volume: 147
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1998.3446

✦ Synopsis

We consider a system of linear partial neutral functional differential equations with nondense domain. A natural generalized notion of solutions is provided by the integral solutions. We derive a variation-of-constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract Volterra integral equation. The basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup.

1998 Academic Press defined on a general Banach space X, where 0<h 1 <h 2 < } } } <h n =h are given real numbers and C X :=C([&h, 0], X ) denotes the space of continuous functions from [&h, 0] to X with the uniform convergence topology. Let article no. DE983446