Existence and decay of solutions of an abstract second order nonlinear problem

In this paper we consider the following nonlinear evolution problem with damping:(∗)|u″(t)+Au(t)+Bαu′(t)=0,t>0,u(0)=u0,u′(0)=u1 where A is a monotone nonlinear operator, Bα a linear operator and α a real number with 0<α⩽1. We study the global existence and decay of solutions of problem (∗).