ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let H be a real Hilbert space, ϕ:H → [0, + ∞] a proper l.s.c., convex function with Lk:={u ε H; ∥u∥2 + ϕ(u) ≦ k} compact for every k 〉 0, let τ 〉 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 $$\begin{gathered} u'(t) + \partial \varphi (u(t)) \in F(t,u(t), u_t ), 0〈 t〈 T \hfill \\ u(s) = v(s), - \tau \leqq s \leqq 0, \hfill \\ \end{gathered} $$ , where F: [0, T] × D(∂ϕ) × $$C_{\partial _\varphi } $$ ([−τ, 0]; H) → H satisfies a certain demiclosedness condition, while v ε $$C_{\partial _\varphi } $$ ([−τ, 0]; H), v(0) ε D(ϕ) and $$\mathop \smallint \limits_{ - \tau }^0 ||\partial \varphi ^0 (v(s))||^2 ds〈 + \infty $$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01762791
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