Electron. J. Diff. Eqns., Vol. 2005(2005), No. 14, pp. 1-8.

Existence of solutions to a paratingent equation with delayed argument

Lotfi Boudjenah

In this work we prove the existence of solutions of a class of paratingent equations with delayed argument,
 (Pt\;x)(t)\subset F([x]_{t})\quad\hbox{for } t\geq 0  
with the initial condition $x(t)=\xi (t)$ for $t\leq 0$. We use a fixed point theorem to obtain a solution and then provide an estimate for the solution.

Submitted December 6, 2004. Published January 30, 2005.
Math Subject Classifications: 34A60, 49J24, 49K24.
Key Words: Convex delayed argument; differential inclusion; paratingent; set-valued function; upper semi-continuity.

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Lotfi Boudjenah
Département de Mathématiques
Université d'Oran
BP 1524, Oran 31000, Algeria
email: lotfi.boudjenah@univ-oran.dz

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