Nonconvex second-order differential inclusions with memory

Abstract

We prove several existence theorems for the second-order differential inclusion of the form\(\dot x(t) \in G(x(t)), \ddot x(t) \in - N_{G(x(t))} \dot x(t) + F(t,T(t)x)\) in the case whenF or bothG andF are maps with nonconvex values in an Euclidean or Hilbert space andF(t, T(t)x) is a memory term ([T(t)x](θ)=x(t+θ)).