Oscillation criteria for third-order semi-canonical differential equations with unbounded neutral coefficients

Karunamurthy Saranya, Veeraraghavan Piramanantham, Ethiraju Thandapani, Ercan Tunç

Abstract


In this paper, we investigate the oscillatory behavior of solutions to a class of third-order differential equations of the form

\[\mathcal{L}z(t)+f(t)y^\beta(\sigma(t))=0\]

where \(\mathcal{L}z(t)=(p(t)(q(t)z^{\prime}(t))^{\prime})^{\prime}\) is a semi-canonical operator and \(z(t)=y(t)+g(t)y(\tau(t))\). The main idea is to convert the semi-canonical operator into canonical form and then obtain some new sufficient conditions for the oscillation of all solutions. The obtained results essentially improve and complement to the known results. Examples are provided
to illustrate the main results.


Keywords


Oscillation, third-order, semi-canonical, unbounded neutral coefficients

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2024.1.08

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