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  • Research Article
  • Open Access

Asymptotic Behavior of Solutions to Some Homogeneous Second-Order Evolution Equations of Monotone Type

Journal of Inequalities and Applications20072007:072931

  • Received: 7 November 2006
  • Accepted: 12 April 2007
  • Published:


We study the asymptotic behavior of solutions to the second-order evolution equation a.e. , , where is a maximal monotone operator in a real Hilbert space with nonempty, and and are real-valued functions with appropriate conditions that guarantee the existence of a solution. We prove a weak ergodic theorem when 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 or the function .


  • Hilbert Space
  • Asymptotic Behavior
  • Evolution Equation
  • Convergence Theorem
  • Additional Assumption


Authors’ Affiliations

Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
Department of Mathematics, Tarbiat Modares University, P.O. Box, 14115-175 Tehran, Iran


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© B. D. Rouhani and H. Khatibzadeh 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.