Oscillatory behavior of solutions of third order semi-canonical dynamic equations on time scale
This paper investigates the oscillatory behavior of nonlinear third-order dynamic equations
on time scales. Our main approach is to transform the equation from its semi-canonical form into a
more tractable canonical form. This transformation simplifies the analysis of oscillation behavior and
allows us to derive new oscillation criteria. These criteria guarantee that all solutions to the equation
oscillate. Our results extend and improve upon existing findings in the literature, particularly for the
special cases where T = R and T = Z . Additionally, we provide illustrative examples to demonstrate
the practical application of the developed criteria.
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