Nonlinear Analysis: Theory, Methods & Applications
Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales
Journal of Computational and Applied Mathematics
Oscillation of delay differential equations on time scales
Mathematical and Computer Modelling: An International Journal
Asymptotic properties of solutions of certain third-order dynamic equations
Journal of Computational and Applied Mathematics
Oscillation of third-order neutral differential equations
Mathematical and Computer Modelling: An International Journal
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It is the purpose of this paper to give oscillation criteria for the third order nonlinear delay dynamic equation (a(t){[r(t)x^@D(t)]^@D}^@c)^@D+f(t,x(@t(t)))=0, on a time scale T, where @c=1 is the quotient of odd positive integers, a andr are positive rd-continuous functions on T, and the so-called delay function @t:T-T satisfies @t(t)@?t for t@?T and lim"t"-"~@t(t)=~ and f@?C(TxR,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=q^N^"^0 and T=N^2 our oscillation results are essentially new. Some examples are given to illustrate the main results.