Open Access

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

Journal of Inequalities and Applications20072007:072931

https://doi.org/10.1155/2007/72931

Received: 7 November 2006

Accepted: 12 April 2007

Published: 6 June 2007

Abstract

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 .

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, University of Texas at El Paso
(2)
Department of Mathematics, Tarbiat Modares University

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Copyright

© 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.