Abstract
For first order nonlinear delay differential equations, necessary and sufficient conditions are established for the oscillation of all proper solutions as well as for the existence of at least one vanishing at infinity proper Kneser solution.
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: FR/317/5-101/12
Funding statement: Supported by the Shota Rustaveli National Science Foundation (Project # FR/317/5-101/12).
References
1 Á. Elbert and I. P. Stavroulakis, Oscillation and nonoscillation criteria for delay differential equations, Proc. Amer. Math. Soc. 123 (1995), 5, 1503–1510. 10.1090/S0002-9939-1995-1242082-1Search in Google Scholar
2 P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, 1964. Search in Google Scholar
3 I. T. Kiguradze, The capability of certain solutions of ordinary differential equations to oscillate (in Russian), Dokl. Akad. Nauk USSR 144 (1962), 33–36; translation in Sov. Math. Dokl. 3 (1962), 649-652. Search in Google Scholar
4 I. T. Kiguradze, On the question of variability of solutions of nonlinear differential equations (in Russian), Differ. Uravn. 1 (1965), 995–1006; translation in Differ. Equ. 1 (1965), 773–782. Search in Google Scholar
5 I. T. Kiguradze, Conditions for the conjugacy of the solutions of nonlinear ordinary differential equations, I (in Russian), Differ. Uravn. 10 (1974), 1387–1399; translation in Differ. Equations 10 (1974), 1073–1082. Search in Google Scholar
6 I. T. Kiguradze, Conditions for the conjugacy of the solutions of nonlinear ordinary differential equations, II (in Russian), Differ. Uravn. 10 (1974), 1586–1594; translation in Differ. Equations 10 (1974), 1224–1230. Search in Google Scholar
7 M. Kon, Y. G. Sficas and I. P. Stavroulakis, Oscillation criteria for delay equations, Proc. Amer. Math. Soc. 128 (2000), 10, 2989–2997. 10.1090/S0002-9939-00-05530-1Search in Google Scholar
8 R. G. Koplatadze, The oscillating solutions of nonlinear first order differential equations with retarded argument (in Russian), Soobshch. Akad Nauk Gruzin. USSR 70 (1973), 17–20. Search in Google Scholar
9 R. G. Koplatadze and T. A. Chanturiya, Oscillation Properties of Differential Equations with Deviating Argument (in Russian), Tbilisi University Press, Tbilisi, 1977. Search in Google Scholar
10 R. G. Koplatadze and T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument (in Russian), Differ. Uravn. 18 (1982), 8, 1463–1465. Search in Google Scholar
11 I. P. Stavroulakis, Oscillation criteria for delay and difference equations with non-monotone arguments, Appl. Math. Comput. 226 (2014), 661–672. 10.1016/j.amc.2013.10.041Search in Google Scholar
© 2016 by De Gruyter