Elvan Akın

Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Abstract We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Oscillatory behavior of solutions of third-order delay and advanced dynamic equations

In this paper, we consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time scales. A time scale is a nonempty closed subset of the real numbers. Examples will be given to illustrate some of the results.MSC:34N05, 39A10, 39A21.

Qualitative Analysis on Differential, Fractional Differential, and Dynamic Equations and Related Topics

1Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Giza, Egypt 2Department of Mathematics, Faculty of Science, University of Hail, Hail 2440, Saudi Arabia 3Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt 4School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China 5Missouri University of Science Technology, 310 Rolla Building, Rolla, MO 65409-0020, USA

Asymptotic Behavior of Certain Integrodifferential Equations

This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.

Comparison criteria for third order functional dynamic equations with mixed nonlinearities

In this paper, we investigate comparison criteria for third order nonlinear dynamic equations with mixed nonlinearities on time scales. Our results are essentially new. Some applications illustrating the importance of our results are included and these applications solve a problem posed in 2, Remark 3.3.