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Oscillation of second order differential equations with advanced argument. (English) Zbl 0858.34057
The author considers second-order functional differential equations with advanced argument of the form $(r^{-1}(t)u'(t))'+p(t)u(t)+q(t) u(\tau(t))=0,\tag{1}$ where $$r,p,q,\tau\in C([t_0,\infty),\mathbb{R})$$, $$r$$ and $$q$$ are positive, $$p$$ is nonnegative and $$\tau(t)\geq t$$. A sufficient condition for the oscillation of (1) is presented here by comparing this equation with the first-order advanced equation of the form $$z'(t)-s(t)z(\tau(t))=0$$.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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##### References:
 [1] ELBERT A., STAVROULAKIS I. P.: Oscillations of the fìrst order differential equations with deviating arguments. Univ. of Ioannina, Technical report No. 172 Math. · Zbl 0832.34064 [2] DŽURINA J.: Asymptotic properties of n-th order differential equations. · Zbl 0817.34039 [3] KIGURADZE I. T.: On the oscillation of solutions of the equation $$d^m u/dt^m + a(t)|u|^n \sgn u = 0$$. (Russian), Mat. Sb. 65 (1964), 172-187. · Zbl 0135.14302 [4] OLÁH R.: Note on the oscillation of differential equation with advanced argument. Math. Slovaca 33 (1981), 241-248. [5] KUSANO T.: On strong oscillation of even order differential equations with advanced arguments. Hiroshima Math. J. 11 (1981), 617-620. · Zbl 0498.34051 [6] LADDE G. S., LAKSHMIKANTHAM V., ZHANG B. G.: Oscillation Theory of Differential Equations with Deviating Arguments. Dekker, New York, 1987. · Zbl 0832.34071 [7] MAHFOUD W. E.: Comparison theorems for delay differential equations. Pacific J. Math. 83 (1979), 187-197. · Zbl 0441.34053 [8] ŠEDA V.: Nonosdilatory solutions of differential equations with deviating argument. Czechoslovak Math. J. 36 (1984), 93-107. · Zbl 0603.34064
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