Perturbation non convexe d'un problème d'évolution dans un espace hilbertien (Q799920)

In the present paper the following evolution equation: \[ -\dot X(t)\in N_{\Gamma (t)}(X(t))+F(t,X(t)),\quad t\in [0,1],\quad X(0)=a\in\Gamma (0) \] is considered, where \(\Gamma\) is a multivalued mapping of the interval [0,1] into the class of nonempty closed convex subsets of a separable Hilbert space H, while F is a multivalued mapping, uniformly continuous on the graph of \(\Gamma\), whose values are nonempty compact subsets of H. Under other additional assumptions, the author shows that the above equation has solutions.