Article

Oscillation of third order nonlinear delay dynamic equations on time scales

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
Mathematical and Computer Modelling 01/2009; 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.

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May 27, 2014