On Differentiability of Solutions with Respect to Parameters in State-Dependent Delay Equations

✍ Scribed by Ferenc Hartung; Janos Turi

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 573 KB
• Volume: 135
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.3238

✦ Synopsis

In this paper we study differentiability of solutions with respect to parameters in state-dependent delay equations. In particular, we give sufficient conditions for differentiability of solutions in the W 1, p norm (1 p< ). In establishing our main results we make use of a version of the Uniform Contraction Principle for quasi-Banach spaces. 1997 Academic Press with respect to (wrt) parameters of the equation. Here % # 3 and _ # 7 represent parameters in the equation ( f ) and in the delay function, {, where 3 and 7 are normed linear spaces with norms | } | 3 and | } | 7 , respectively. In this paper we restrict our attention to differentiability of solutions wrt the parameters ., % and _. The notation x t denotes the solution article no.