On the existence of monotone solutions for second-order non-convex differential inclusions in infinite dimensional spaces (Q1888646)

The authors prove the existence of monotone solutions for a second-order nonconvex-valued differential inclusion \[ x''(t)\in F(x(t),x'(t)), \quad a.e \text{ on } [0,T],\quad (x(0),x'(0))=(x_0,y_0)\in K\times \Omega, \] where \(F:K\times \Omega\to {\mathcal P}(H)\) is a set-valued function, and \(K\) and \(\Omega\) are nonempty subsets of an infinite-dimensional Hilbert space \(H.\)