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Oscillation theory of first order functional differential equations with deviating arguments. (English) Zbl 0552.34062
From the summary: ”New oscillation criteria are established for the first order functional differential equation (*) $y'(t)+p(t)y(g(t))=0$ and its nonlinear analogue. Possible extension of the results for (*) to equations with several deviating arguments is attempted. Finally, it is shown that there exists a class of autonomous equations for which the oscillation situation can be completely characterized.”
Reviewer: V.Sree Hari Rao

34K99Functional-differential equations
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
Full Text: DOI
[1] C. H. Anderson,Asymptotic oscillation results for solutions to first-order nonlinear differential-difference equations of advanced type, J. Math. Anal. Appl.,24 (1968), pp. 430--439. · Zbl 0191.10703 · doi:10.1016/0022-247X(68)90041-3
[2] R. D. Driver -D. W. Sasser -M. L. Slater,The equation x’(t)=ax(t)+bx(t) with “small{” delay, Amer. Math. Monthly,80 (1973), pp. 990--995. · Zbl 0292.34076 · doi:10.2307/2318773
[3] A. F. Ivanov -V. N. Ševelo,On the oscillation and asymptotic behavior of solutions of differential-functional equations of the first order, Ukrain. Mat. Ž.,33 (1981), pp. 745--751 (Russian). · Zbl 0489.34071
[4] Y. Kitamura -T. Kusano,Oscillations of first-order nonlinear differential equations with deviating arguments, Proc. Amer. Math. Soc.,78 (1980), pp. 64--68. · Zbl 0433.34051 · doi:10.1090/S0002-9939-1980-0548086-5
[5] R. G. Koplatadze,On oscillatory solutions of first order nonlinear differential equations with retarded argument, Soobšč.Akad. Nauk Gruzin. SSR,70 (1973), pp. 17--20 (Russian). · Zbl 0297.34066
[6] R. G. Koplatadze -T. A. Čanturija,On Oscillatory Properties of Differential Equations with Deviating Arguments, Tbilisi Univ. Press, Tbilisi (1977) (Russian).
[7] R. G. Koplatadze -T. A. Čanturija,On oscillatory and monotone solutions of first order differential equations with deviating arguments, Differential’nye Uravnenija,18 (1982), pp. 1463--1465 (Russian). · Zbl 0496.34044
[8] T. Kusano,On even order functional differential equations with advanced and retarded arguments, J. Differential Equations,45 (1982), pp. 75--84. · Zbl 0512.34059 · doi:10.1016/0022-0396(82)90055-9
[9] G. Ladas,Sharp conditions for oscillation caused by delays, Applicable Anal.,9 (1979), pp. 93--98. · Zbl 0407.34055 · doi:10.1080/00036817908839256
[10] G. Ladas -V. Lakshmikantham -J. S. Papadekis,Oscillations of higher-order retarded differential equations generated by the retarded argument, “Delay and Functional Differential Equations and their Applications{” (K. Schmitt, Ed.), pp. 219--231, Academic Press, New York (1972).
[11] G. Ladas -I. P. Stavroulakis,On delay differential inequalities of first order, Funkcial. Ekvac.,25 (1982), pp. 105--113. · Zbl 0492.34060
[12] G. Ladas -I. P. Stavroulakis,Oscillations caused by several retarded and advanced arguments, J. Differential Equations,44 (1982), pp. 134--152. · Zbl 0477.34050 · doi:10.1016/0022-0396(82)90029-8
[13] G. Ladas -Y. G. Sficas -I. P. Stavroulakis,Necessary and sufficient conditions for oscillations, Amer. Math. Monthly,90 (1983), pp. 637--640. · Zbl 0526.34054 · doi:10.2307/2323283
[14] G.Ladas - Y. G.Sficas - I. P.Stavroulakis,Functional differential inequalities and equations with oscillating coefficients, Proceedings of the Fifth International Conference on “Trends in Theory and Practice of Nonlinear Differential Equations{” held at Arlington, Texas during June 14--18, 1982 (to appear).
[15] J. C. Lillo,Oscillatory solutions of the equation y’(x)=m(x)(x(x)), J. Differential Equations,6 (1969), pp. 1--35. · Zbl 0174.39804 · doi:10.1016/0022-0396(69)90114-4
[16] H. Onose,Oscillation of a functional differential equation arising from an industrial problem, J. Austral. Math. Soc. (Series A),26 (1978), pp. 323--329. · Zbl 0402.34021 · doi:10.1017/S1446788700011848
[17] H. Onose,Oscillatory properties of first order differential inequalities with deviating argument, Funkcial. Ekvac.,26 (1983), pp. 189--195. · Zbl 0525.34051
[18] V. N.Ševelo - A. F.Ivanov,On the asymptotic behavior of solutions of a class of first order differential equations with deviating argument of mixed type, “Asymptotic Behavior of Functional-Differential Equations{”, Kiev (1978), pp. 145--150 (Russian).
[19] W. E. Shreve,Oscillation in first order nonlinear retarded argument differential equations, Proc. Amer. Math. Soc.,41 (1973), pp. 565--568. · Zbl 0254.34075 · doi:10.1090/S0002-9939-1973-0372371-X
[20] I. P. Stavroulakis,Nonlinear delay differential inequalities, Nonlinear Anal.,6 (1982), pp. 389--396. · Zbl 0488.34062 · doi:10.1016/0362-546X(82)90024-4
[21] A. Tomaras,Oscillations of an equation relevant to an industrial problem, Bull. Austral. Math. Soc.,12 (1975), pp. 425--431. · Zbl 0299.34101 · doi:10.1017/S0004972700024084
[22] A. Tomaras,Oscillatory behaviour of an equation arising from an industrial problem, Bull. Austral. Math. Soc.,13 (1975), pp. 255--260. · Zbl 0315.34091 · doi:10.1017/S0004972700024448
[23] A. Tomaras,Oscillatory behaviour of first order delay differential equations, Bull. Austral. Math. Soc.,19 (1978), pp. 183--190. · Zbl 0397.34093 · doi:10.1017/S0004972700008662
[24] M. I. Tramov,Conditions for oscillatory solutions of first order differential equations with a delayed argument, Izv. Vysš. Učebn. Zaved. Matematika, no. 3 (154) (1975), pp. 92--96 (Russian). · Zbl 0319.34070