Existence for a doubly nonlinear Volterra equation

We consider a doubly nonlinear Volterra equation involving a nonsmooth kernel and two possibly degenerate monotone operators. By exploiting an implicit time-discretization procedure, we obtain the existence of a global strong solution and extend to the nonlocal in time situation some former results by Colli [P. Colli, On some doubly nonlinear evolution equations in Banach spaces, Japan J. Indust. Appl. Math. 9 (2) (1992) 181–203]. © 2006 Elsevier Inc. All rights reserved