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)∈Au(t),a. e. onR+,u(0)=u0,supt≥0|u(t)|<+∞, to a zero of A, without assuming A−1(0)≠0̸, and determine the rate of convergence, where A is a general maximal monotone operator. We present also some applications of our result.