Existence of Solutions for a Class of Damped Vibration Problems on Time ScalesReport as inadecuate




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Advances in Difference Equations

, 2010:727486

First Online: 06 December 2010Received: 03 June 2010Revised: 20 November 2010Accepted: 24 November 2010

Abstract

We present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a class of damped vibration problems on time scale Open image in new window, Open image in new windowOpen image in new window-a.e. Open image in new window, Open image in new window where Open image in new window denotes the delta or Hilger derivative of Open image in new window at Open image in new window, Open image in new window, Open image in new window is the forward jump operator, Open image in new window is a positive constant, Open image in new window, Open image in new window, and Open image in new window. By establishing a proper variational setting, three existence results are obtained. Finally, three examples are presented to illustrate the feasibility and effectiveness of our results.

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Author: Yongkun Li - Jianwen Zhou

Source: https://link.springer.com/







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