Non-degenerate Implicit Evolution Inclusions

Abstract

We prove the existence of solutions for the implicit evolution inclusion (B(t)u(t))' + A(t,u(t)) ∋ ƒ(t) under conditions that are easy to verify on the set valued operator A(t, ‧) and that do not imply the operator is monotone. We also present an example where our existence theorem applies to a time dependent implicit inclusion.