On the structure of the solution set of evolution inclusions with Fréchet subdifferentials (Q1566584)

The following Cauchy problem is studied \[ x'\in -{\partial}^-f(x) + F(t,x),\quad x(0)=x_0, \] where \(f:\Omega \rightarrow \mathbb{R}\cup \{+\infty\}\) (\(\Omega \) is an open subset of a separable Hilbert space \(H\)) has a \(\phi\)-monotone subdifferential of order two, \(\partial^-f\) is the Frechet subdifferential of \(f\), and \(F\) is a multifunction with nonempty, closed and convex values. Under appropriate assumptions, the author proves the existence of a nonempty solution set, which is an \(R_{\delta}\) set. In addition, a Kneser-type theorem is established, and the continuity of the solution multifunction is proved. An application to a periodic problem is given.