A note on the strong convergence of solutions to a second order evolution equation

In this note, with suitable assumptions on p(t) and r(t), we establish the strong convergence of solutions to the following nonlinear second order evolution equation {p(t)u '' (t) + r(t)u' (t) is an element of Au(t), a. e. on R+, u(0) = u(0), sup(t >= 0) vertical bar u(t)vertical bar < +infinity, to a zero of A, without assuming A(-1) (0) not equal empty set, and determine the rate of convergence, where A is a general maximal monotone operator. We present also some applications of our result. (C) 2012 Elsevier Inc. All rights reserved.