Coupled problems driven by time and state-dependent maximal monotone operators.

We are concerned in this paper with a new class of coupled problems by differential inclusions involving time and state-dependent maximal monotone operators with perturbations. The operators vary (in the sense of the pseudo-distance) in an absolutely continuous way in time, and in a Lipschitz-continuous way in state. By a discretization technique, we state the well-posedness (existence and uniqueness of the solution) in a real separable Hilbert space. Applications to optimal control and to fractional theory are provided. [ABSTRACT FROM AUTHOR]