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Oscillation criteria for certain third-order variable delay functional dynamic equations on time scales. (English) Zbl 1298.34178

Summary: The oscillation of certain third-order nonlinear variable delay functional dynamic equations with nonlinear neutral on time scales is discussed in this article. By using the generalized Riccati transformation and a lot of inequality techniques, some new oscillation criteria for the equations are established. Many of the results are new for the corresponding third-order difference equations and differential equations are as special cases. Some examples are given to illustrate the importance of our results.

MSC:

34N05 Dynamic equations on time scales or measure chains
34K11 Oscillation theory of functional-differential equations
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
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