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Asymptotic properties of solutions of third-order nonlinear differential equations with deviating argument. (English) Zbl 1151.34053
Summary: We consider the third-order nonlinear differential equation with deviating argument of the form
\[ \left(\frac{1}{p(t)}\left(\frac{1}{r(t)}\,x'(t)\right)'\right)'+q(t)f(x(\omega(t)))=0,\quad t\geq a \]
and a more general differential equation with mixed argument of the form
\[ \left(\frac{1}{p(t)}\left(\frac{1}{r(t)}\,x'(t)\right)'\right)'+q_1(t)f_1(x(g(t)))+q_2(t)f_2(x(h(t))) =0,\quad t\geq a. \]
The aim of this paper is to establish comparison principles, between a nonlinear differential equation of the third order with deviating argument (with delay, advanced or mixed argument) and the corresponding linear equation without deviating argument.

MSC:
34K11 Oscillation theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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