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

AbstractIn this paper, we establish the strong convergence of possible solutions to the following nonhomogeneous second order evolution system{u″(t)+cu′(t)∈Au(t)+f(t)a.e. t∈(0,+∞),u(0)=u0,supt⩾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