A strong convergence theorem for solutions to a nonhomogeneous second order evolution equation

In this paper, we establish the strong convergence of possible solutions to the following nonhomogeneous second order evolution system { u ″ ( t ) + c u ′ ( t ) ∈ A u ( t ) + f ( t ) a.e. t ∈ ( 0 , + ∞ ) , u ( 0 ) = u 0 , sup t ⩾ 0 | u ( t ) | < + ∞ to an element of A − 1 ( 0 ) , with an exponential rate of convergence when f ≡ 0 , where A is a general maximal monotone operator in a real Hilbert space H, c > 0 is a real constant and f : R + → H is a given function. We show also that the curve u is almost nonexpansive, and present some applications of our result.