Investigating Oscillations in Higher-Order Half-Linear Dynamic Equations on Time Scales
This study presents novel and generalizable sufficient conditions for determining
the oscillatory behavior of solutions to higher-order half-linear neutral delay dynamic
equations on time scales. Utilizing the Riccati transformation technique in combination
with Taylor monomials, we derive new and comprehensive oscillation criteria that cover
a wide range of cases, including super-linear, half-linear, and sublinear equations. These
results extend and improve upon existing oscillation criteria found in the literature by
introducing more general conditions and providing a broader applicability to different
types of dynamic equations. Furthermore, the study highlights the role of symmetry
in the underlying equations, demonstrating how symmetry properties can be leveraged
to simplify the analysis and provide additional insights into oscillatory behavior. To
demonstrate the practical relevance of our findings, we include illustrative examples that
show how these new criteria, along with symmetry-based perspectives, can be effectively
applied to various time scales.
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This study presents novel and generalizable sufficient conditions for determining
the oscillatory behavior of solutions to higher-order half-linear neutral delay dynamic
equations on…
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