Abstract
By the Riccati transformation technique, we study some new oscillatory properties for the second-order dynamic equation on an arbitrary time scale mathbb {T}. We also establish the Kamenev-type and Philos-type oscillation criteria. At the end, we give examples which illustrate our main results.
Highlights
In [25], Kubyshkin and Moryakova considered a secondorder differential–difference equation of delay type x€ðtÞ þ Ax_ðtÞ þ xðtÞ þ Kðxðt À hÞÞ þ Wðx_ðt À hÞÞ 1⁄4 0; ð1:1Þ ki; wj 2 R, respectively
By the Riccati transformation technique, we study some new oscillatory properties for the second-order dynamic equation on an arbitrary time scale T: We establish the Kamenev-type and Philos-type oscillation criteria
By using an integral averaging technique of Kamenev-type, we present some new oscillation criteria of (1.2)
Summary
In [25], Kubyshkin and Moryakova considered a secondorder differential–difference equation of delay type x€ðtÞ þ Ax_ðtÞ þ xðtÞ þ Kðxðt À hÞÞ þ Wðx_ðt À hÞÞ 1⁄4 0; ð1:1Þ ki; wj 2 R, respectively. Without loss of generality, we assume that y(t) is an eventually positive solution of (1.2) i.e., there exists t0 s0 such that yðtÞ [ 08t 2 1⁄2s01ÞT: A similar argument holds for the case when y(t) is eventually negative. Without loss of generality, we assume that y(t) is an eventually positive function, i.e., there exists t0 such that yðtÞ [ 08t 2 1⁄2t01ÞT: A similar argument holds for the case when y(t) is eventually negative.
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