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Oscillation and nonoscillation criteria for delay differential equations. (English) Zbl 0828.34057
The equation $$x'(t)+ p(t) x(\tau(t))= 0$$, $$t\geq t_0$$, is considered with $$p(t)\geq 0$$, $$\tau(t)< t$$ for $$t\geq t_0$$, $$\lim_{t\to +\infty} \tau(t)= +\infty$$. Sufficient conditions are obtained for every proper solution of this equation to be oscillatory. They make more precise in a certain sense some earlier results.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
oscillatory
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##### References:
 [1] Á. Elbert, Comparison theorem for first-order nonlinear differential equations with delay, Studia Sci. Math. Hungar. 11 (1976), no. 1-2, 259 – 267 (1978). · Zbl 0438.34062 [2] Á. Elbert and I. P. Stavroulakis, Oscillations of first order differential equations with deviating arguments, Recent trends in differential equations, World Sci. Ser. Appl. Anal., vol. 1, World Sci. Publ., River Edge, NJ, 1992, pp. 163 – 178. · Zbl 0832.34064 [3] R. G. Koplatadze and T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial$$^{\prime}$$nye Uravneniya 18 (1982), no. 8, 1463 – 1465, 1472 (Russian). · Zbl 0496.34044 [4] Gerasimos Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), no. 2, 93 – 98. · Zbl 0407.34055 [5] A. D. Myškis, Linear homogeneous differential equations of the first order with retarded argument, Uspehi Matem. Nauk (N.S.) 5 (1950), no. 2(36), 160 – 162 (Russian). · Zbl 0041.42108 [6] Линейные дифференциал$$^{\приме}$$ные уравнения с запаздывающим аргументом, 2нд ед., Издат. ”Наука”, Мосцощ, 1972 (Руссиан).
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