Electron. J. Diff. Equ., Vol. 2014 (2014), No. 105, pp. 1-12.

Oscillatory and asymptotic behavior of solutions for second-order nonlinear integro-dynamic equations on time scales

Ravi P. Agarwal, Said R. Grace, Donal O'Regan, Agacik Zafer

In this article, we study the asymptotic behavior of non-oscillatory solutions of second-order integro-dynamic equations as well as the oscillatory behavior of forced second order integro-dynamic equations on time scales. The results are new for the continuous and discrete cases. Examples are provided to illustrate the relevance of the results.

Submitted September 11, 2013. Published April 15, 2014.
Math Subject Classifications: 34N05, 45D05, 34C10.
Key Words: Integro-dynamic equation; oscillation; time scales.

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Ravi P. Agarwal
Department of Mathematics
Texas A&M University - Kingsville
Kingsville, TX 78363, USA
email: agarwal@tamuk.edu
  Said R. Grace
Department of Engineering Mathematics, Faculty of Engineering
Cairo University, Orman, Giza 12221, Egypt
email: saidgrace@yahoo.com
Donal O'Regan
School of Mathematics, Statistics and Applied mathematics
National University of Ireland, Galway, Ireland
email: donal.oregan@nuigalway.ie
Agacik Zafer
College of Engineering and Technology
American University of the Middle East
Block 3, Egaila, Kuwait
email: agacik.zafer@gmail.com

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