Article

# Oscillation of third order nonlinear delay dynamic equations on time scales

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
(Impact Factor: 1.41). 04/2009; 49(7-8):1573-1586. DOI: 10.1016/j.mcm.2008.12.011
Source: DBLP

ABSTRACT

It is the purpose of this paper to give oscillation criteria for the third order nonlinear delay dynamic equation on a time scale T, where γ≥1 is the quotient of odd positive integers, a and are positive rd-continuous functions on T, and the so-called delay function τ:T→T satisfies τ(t)≤t for t∈T and limt→∞τ(t)=∞ and f∈C(T×R,R). Our results are new for third order delay dynamic equations and extend many known results for oscillation of third order dynamic equation. These results in the special cases when T=R and T=N involve and improve some oscillation results for third order delay differential and difference equations; when T=hN, T=qN0 and T=N2 our oscillation results are essentially new. Some examples are given to illustrate the main results.

### Full-text

Available from: Taher S. Hassan, Mar 28, 2014
• Source
• "Agarwal et al. [1], Hassan [12], and Li et al. [15] considered a third-order nonlinear delay dynamic equation "
##### Article: Oscillation Theorems for Fourth-Order Half-Linear Delay Dynamic Equations with Damping
[Hide abstract]
ABSTRACT: This article is concerned with oscillatory behavior of a class of fourth-order half-linear delay dynamic equations with damping on a time scale. Some new oscillation criteria are established.
Mediterranean Journal of Mathematics 05/2014; 11(2). DOI:10.1007/s00009-013-0310-0 · 0.66 Impact Factor
• Source
• "The results improve and extend the oscillation criteria established in [8] [10] [11] [12] [13] [16] [18] [24] [25] [26]. "
##### Article: Asymptotic behavior of third order functional dynamic equations with γ-Laplacian and nonlinearities given by Riemann-Stieltjes integrals

Electronic Journal of Qualitative Theory of Differential Equations 01/2014; DOI:10.14232/ejqtde.2014.1.40 · 0.82 Impact Factor
• Source
• "respectively, and established some sufficient conditions for oscillation. Hassan [24] studied the third-order dynamic equations (í µí± (í µí±¡) {[í µí± (í µí±¡) í µí±¥ "
##### Article: Oscillation for Higher Order Dynamic Equations on Time Scales
[Hide abstract]
ABSTRACT: We investigate the oscillation of the following higher order dynamic equation: , on some time scale , where , and are positive rd-continuous functions on and are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.
Abstract and Applied Analysis 10/2013; 2013. DOI:10.1155/2013/268721 · 1.27 Impact Factor