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Article . 2019
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OSCILLATORY BEHAVIOROF NONLINEAR ADVANCED DIFFERENTIAL EQUATIONS WITH A NON-MONOTONE ARGUMENT

Oscillatory behavior of nonlinear advanced differential equations with a non-monotone argument
Authors: Öcalan, Özkan; Kılıç, Nurten; Özkan, Umut Mutlu;

OSCILLATORY BEHAVIOROF NONLINEAR ADVANCED DIFFERENTIAL EQUATIONS WITH A NON-MONOTONE ARGUMENT

Abstract

Summary: Consider the first-order nonlinear advanced differential equation \[ x'(t)-p(t)f(x(\tau(t)))=0,\quad t\ge t_0, \] where \(p(t)\) is are nonnegative function on \(\mathbb R\) and \(\tau(t)\) is non-monotone or nondecreasing function such that \(\tau(t)\ge t\) for \(t\ge t_0\). Under these assumptions we researched oscillatory behaviour of solutions of nonlinear advanced differential equations and we obtain new oscillation criteria, involving limsup and liminf. An example illustrating the result is also given.

Country
Turkey
Keywords

non-oscillatory solution, Non-monotone argument, Non-Monotone Argument, non-monotone argument, Oscillatory solution, Advanced differential equation, Advanced Differential Equation, advanced differential equation, oscillatory solution, Oscillatory Solution, Oscillation theory of functional-differential equations, Non-Oscillatory Solution, Non-oscillatory solution

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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