Taiwanese Journal of Mathematics

OSCILLATION THEOREMS RELATED TO AVERAGING TECHNIQUE FOR SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

Zhiting Xu

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Abstract

Some oscillation theorems are established by the averaging technique for the second order nonlinear neutral delay differential equation $$ \begin{array}{l} (r(t) |x^{\prime}(t)|^{\gamma-1} x^{\prime}(t))^{\prime} + q_1(t) |y(t-\sigma_1)|^{\alpha-1} y(t-\sigma_1) \\ \hspace{5mm} + q_2(t) |y(t-\sigma_2)|^{\beta-1} y(t-\sigma_2) = 0, \quad t \geq t_0, \end{array} $$ where $x(t) = y(t) + p(t) y(t-\tau)$, $\tau$, $\sigma_1$ and $\sigma_2$ are nonnegative constants, $\alpha$, $\beta$ and $\gamma$ are positive constants, and $r$, $p$, $q_1$, $q_2 \in C([t_0, \infty), \mathbb{R})$. The results obtained here essentially improve some known results in the literature. In particular, two interesting examples that point out the applications of our results are also included.

Article information

Source
Taiwanese J. Math., Volume 11, Number 4 (2007), 1221-1235.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404815

Digital Object Identifier
doi:10.11650/twjm/1500404815

Mathematical Reviews number (MathSciNet)
MR2348564

Zentralblatt MATH identifier
1140.34416

Subjects
Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34C15: Nonlinear oscillations, coupled oscillators

Keywords
oscillation neutral differential equation nonlinear averaging technique second order

Citation

Xu, Zhiting. OSCILLATION THEOREMS RELATED TO AVERAGING TECHNIQUE FOR SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS. Taiwanese J. Math. 11 (2007), no. 4, 1221--1235. doi:10.11650/twjm/1500404815. https://projecteuclid.org/euclid.twjm/1500404815


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