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Oscillation behavior of solutions of third-order nonlinear delay dynamic equations on time scales

Zhenlai Han|Tongxing Li|Shurong Sun|Meng Zhang
대한수학회 (The Korean Mathematical Society)|2011.07|대한수학회논문집 (Communications of the KMS)|제26권 제3호|pp. 499-513

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참고문헌

키워드

time scalesoscillation behaviorthird order delay dynamic equations
주제분류수학

초록

By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations (c(t)(p^(t)x^Δ(t))^Δ)^Δ + q(t)f(x(τ(t)))=0on a time scale T, where c(t), p(t) and q(t) are real-valued positive rd-continuous functions defined on T. We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our oscillation results are essentially new. Some examples are considered to illustrate the main results.

Abstract

By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations (c(t)(p^(t)x^Δ(t))^Δ)^Δ + q(t)f(x(τ(t)))=0on a time scale T, where c(t), p(t) and q(t) are real-valued positive rd-continuous functions defined on T. We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our oscillation results are essentially new. Some examples are considered to illustrate the main results.

참고문헌 (22)

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