Oscillatory behavior of solutions of certain third order mixed neutral differential equations
2013 ◽
Vol 44
(1)
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pp. 99-112
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Keyword(s):
The objective of this paper is to study the oscillatory and asymptotic properties of third order mixed neutral differential equation of the form $$ (a(t) [x(t) + b(t) x(t - \tau_{1}) + c(t) x(t + \tau_{2})]'')' + q(t) x^{\alpha}(t - \sigma_{1}) + p(t) x^{\beta}(t + \sigma_{2}) = 0 $$where $a(t), b(t), c(t), q(t)$ and $p(t)$ are positive continuous functions, $\alpha$ and $\beta$ are ratios of odd positive integers, $\tau_{1}, \tau_{2}, \sigma_{1}$ and $\sigma_{2}$ are positive constants. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converge to zero. Some examples are provided to illustrate the main results.
2005 ◽
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2016 ◽
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pp. 1-8
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1992 ◽
Vol 46
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pp. 149-157
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1992 ◽
Vol 52
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