On second-order functional differential inclusions in Hilbert spaces (Q2913831)

This paper is devoted to prove the existence of monotone solutions, in a Hilbert space, to the Cauchy problem NEWLINE\[NEWLINE \ddot{x}(t)\in f(t,T(t)x,\dot x(t))+F(T(t)x,\dot x(t))\text{ a.e. on } [0,\tau ],NEWLINE\]NEWLINE NEWLINE\[NEWLINE x(s)=\varphi (s)\;\forall\, s\in [-a,0],NEWLINE\]NEWLINE NEWLINE\[NEWLINE x(s)\in P(x(t))\;\forall\, t\in [0,\tau ],\;\forall \, s\in [t,\tau ],NEWLINE\]NEWLINE where \(F\) is an upper semi-continuous multifunction with compact values contained in the Clarke subdifferential \(\partial _CV(x)\) of a uniformly regular function \(V\), \(f\) is a Carathéodory function and \(P\) is a lower semi-continuous multifunction.