Existence of solutions for a class of damped vibration problems on time scales. (English) Zbl 1216.34102
The authors present in detail the concepts on time scales which are available in the standard book written by Martin Bohner and A. C. Peterson. The time scale is an interesting area of current research as it unifies both continuous and discrete concepts. The authors consider a class of damped vibration problem on time scales with periodic boundary conditions.
The authors use recent methods of variational methods and critical point theory for establishing the existence of solution to the above two point boundary value problem. By taking a variational structure of the problem, the authors reduce the problem of finding solutions to the two point boundary value problem to the one of a corresponding functional. The results of the paper are illustrated with some suitable examples.
These results are extension of their previous paper published in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 5, 1375–1388 (2010; Zbl 1201.46035)].
The authors use recent methods of variational methods and critical point theory for establishing the existence of solution to the above two point boundary value problem. By taking a variational structure of the problem, the authors reduce the problem of finding solutions to the two point boundary value problem to the one of a corresponding functional. The results of the paper are illustrated with some suitable examples.
These results are extension of their previous paper published in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 5, 1375–1388 (2010; Zbl 1201.46035)].
Reviewer: K. Rajendra Prasad (Visakhapatnam)
MSC:
| 34N05 | Dynamic equations on time scales or measure chains |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
Citations:
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