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A class of strongly nonlinear functional differential equations

Authors:

Institution:

1. Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piazzale Europa 1, 34100, Trieste, Italy
2. Department of Mathematics, Polytechnic, Institute of Ia?i R., Ro, Is 1 6600, P. O. Box 180, 6600, Ia?i 6600, R.S. Romania

Abstract:

Let H be a real Hilbert space, phiv

0, +

] a proper l.s.c., convex function with L_k:={u epsi

² +

(u)

k} compact for every k > 0, let tau

> 0 be a given constant and $C_{\partial _\varphi } ( - \tau ,0];H): = \{ v \in C( - \tau ,0];H); v(t) \in D(\partial _\varphi ) a.e. for t \in ( - \tau ,0)\}$ . We prove an existence result for strong solutions to a class of functional differential equations of the form

$\begin{gathered} u'(t) + \partial \varphi (u(t)) \in F(t,u(t), u_t ), 0< t< T \hfill \\ u(s) = v(s), - \tau \leqq s \leqq 0, \hfill \\ \end{gathered}$

Keywords:
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