Nonconvex evolution inclusions governed by the difference of two subdifferentials

The aim of the present paper is to prove the existence result for a class of differential inclusions governed by the difference of two subdifferentials of nonconvex functions in Hilbert spaces. More precisely, by using the Moreau-Yosida regularization, the existence of local solutions for the following differential inclusion (u)over dot(t) + partial derivative Phi(1) (u(t)) - partial derivative Phi(2)(u(t)) is an element of f(t) for almost every t is an element of [0, T-0], u(0) = u(0) is proved, where both functions Phi(1) and Phi(2) are assumed to be primal lower nice uniformly with respect to subgradients.