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Oscillations of differential equation with retarded argument. (English) Zbl 0584.34047
The author gives several sufficient conditions for the oscillation of bounded solutions of $(r(t)y'(t))'+p(t)f(y(\rho_ 1(t)))h(y'(\rho_ 2(t)))=0.$ There is one theorem which guarantees the oscillation of all solutions.
Reviewer: E.Heil
##### MSC:
 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
##### References:
 [1] BRADLEY J. S.: Oscillation theorems for a second order delay equation. J. Diff. Equations 8, 1970, 397-403. · Zbl 0212.12102 [2] GUSTAFSON G. B.: Bounded oscillations of linear and nonlinear delay-differential equations of even order. J. Math. Anal, and Appl. 46, 1974, 175-189. · Zbl 0282.34027 [3] LADA G., LAKSHMIKANTHAM V.: Oscillations caused by retarded actions. Applicable Analysis 4, 1974, 9-15. · Zbl 0334.34059 [4] ODARIČ O. N., SEVELO V. N.: Some problems in the theory of oscillation of second order differential equations with deviating arguments. Ukrainian Math. J. 23, 1971, 508-516. [5] ODARIČ O. N., SEVELO V. N.: The non-oscillations of solutions of non-linear second differential equations with retarded argument. Trudy Sem. Mat. Fiz. Nelin. Kolebanij 1, 1968, 268-279. [6] STAIKOS V. A., PETSOULAS A. G.: Some oscillation criteria for second order non-linear delay differential equations. J. Math. Anal. Appl. 30, 1970, 695-701. · Zbl 0193.06303 [7] STAIKOS V. A.: Oscillatory property of a certain delay differential equation. Bull. Soc. Math. Grese 11, 1970, 1-5. · Zbl 0225.34039 [8] ŠOLTÉS P.: Oscillatory properties of solutions of second order non-linear delay differential equations. Math. Slovaca 31, 1981, 207-215. [9] OHRISKA J.: The argument delay and oscillatory properties of differential equation of n-th order. Czech. Math. J. 29 (104), 1979, 268-283. · Zbl 0396.34058
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