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 ) ∈ A u ( t ) , a. e. on R + , u ( 0 ) = u 0 , sup t ≥ 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.