Time dependent evolution inclusions governed by the difference of two subdifferentials

Abstract

The purpose of this paper is to study evolution inclusions involving time dependent subdifferential operators which are non-monotone. More precisely, we study existence of solutions for the following evolution equation in a real Hilbert space $X$~: $u^\prime (t)+\partial f^t(u(t))-\partial\varphi^t(u(t))\ni w(t)$, $u(0)=u_0$, where $f^t$ and $\varphi^t$ are closed convex proper functions on $X$.

Keywords

• convex and difference convex functions
• evolution inclusion
• subdifferential
• local existence