%0 Journal Article
%T Asymptotic Behavior of Solutions to Some Homogeneous Second-Order Evolution Equations of Monotone Type
%A Behzad Djafari Rouhani
%A Hadi Khatibzadeh
%J Journal of Inequalities and Applications
%D 2007
%I Springer
%R 10.1155/2007/72931
%X We study the asymptotic behavior of solutions to the second-order evolution equation p(t)u ¡é ? 3(t)+r(t)u ¡é ? 2(t) ¡é    Au(t) a.e. t ¡é    (0,+ ¡é    ), u(0)=u0, supt ¡é ¡ë £¤0|u(t)|<+ ¡é    , where A is a maximal monotone operator in a real Hilbert space H with A ¡é   ¡¯1(0) nonempty, and p(t) and r(t) are real-valued functions with appropriate conditions that guarantee the existence of a solution. We prove a weak ergodic theorem when A is the subdifferential of a convex, proper, and lower semicontinuous function. We also establish some weak and strong convergence theorems for solutions to the above equation, under additional assumptions on the operator A or the function r(t).
%U http://dx.doi.org/10.1155/2007/72931