Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
differential equation; non-monotone argument; oscillatory solution; nonoscillatory solution; Grönwall inequality.
differential equation; non-monotone argument; oscillatory solution; nonoscillatory solution; Grönwall inequality.
Summary:
Sufficient oscillation conditions involving $\limsup $ and $\liminf $ for first-order differential equations with non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Grönwall inequality. Examples, numerically solved in MATLAB, are also given to illustrate the applicability and strength of the obtained conditions over known ones.
References:
[1] Braverman, E., Chatzarakis, G.E., Stavroulakis, I.P.: Iterative oscillation tests for differential equations with several non-monotone arguments. Adv. Difference Equ., 87, 2016, MR 3479781
[2] Braverman, E., Karpuz, B.: On oscillation of differential and difference equations with non-monotone delays. Appl. Math. Comput., 218, 7, 2011, 3880-3887, MR 2851485
[3] Chatzarakis, G.E.: Differential equations with non-monotone arguments: Iterative Oscillation results. J. Math. Comput. Sci., 6, 5, 2016, 953-964,
[4] Chatzarakis, G.E.: On oscillation of differential equations with non-monotone deviating arguments. Mediterr. J. Math., 14, 2, 2017, 82, DOI 10.1007/s00009-017-0883-0 | MR 3620160
[5] Chatzarakis, G.E., Jadlovská, I.: Improved iterative oscillation tests for firs-order deviating differential equations. Opuscula Math., 38, 3, 2018, 327-356, DOI 10.7494/OpMath.2018.38.3.327 | MR 3781617
[6] Chatzarakis, G.E., Li, T.: Oscillation criteria for delay and advanced differential equations with non-monotone arguments. Complexity, 2018, 2018, 1-18, Article ID 8237634.. DOI 10.1155/2018/8237634 | MR 3620160
[7] Chatzarakis, G.E., Öcalan, Ö.: Oscillations of differential equations with several non-monotone advanced arguments. Dynamical Systems, 30, 3, 2015, 310-323, DOI 10.1080/14689367.2015.1036007 | MR 3373715
[8] Erbe, L.H., Kong, Qingkai, Zhang, B.G.: Oscillation Theory for Functional Differential Equations. 1995, Monographs and Textbooks in Pure and Applied Mathematics, 190. Marcel Dekker, Inc., New York, MR 1309905
[9] Erbe, L.H., Zhang, B.G.: Oscillation of first order linear differential equations with deviating arguments. Differential Integral Equations, 1, 3, 1988, 305-314, MR 0929918
[10] Fukagai, N., Kusano, T.: Oscillation theory of first order functional-differential equations with deviating arguments. Ann. Mat. Pura Appl., 136, 1, 1984, 95-117, DOI 10.1007/BF01773379 | MR 0765918 | Zbl 0552.34062
[11] Jaro¹, J., Stavroulakis, I.P.: Oscillation tests for delay equations. Rocky Mountain J. Math., 29, 1, 1999, 197-207, DOI 10.1216/rmjm/1181071686 | MR 1687662
[12] Jian, C.: On the oscillation of linear differential equations with deviating arguments. Math. in Practice and Theory, 1, 1, 1991, 32-40, MR 1107456
[13] Kon, M., Sficas, Y.G., Stavroulakis, I.P.: Oscillation criteria for delay equations. Proc. Amer. Math. Soc., 128, 10, 2000, 2989-2998, DOI 10.1090/S0002-9939-00-05530-1 | MR 1694869
[14] Koplatadze, R.G., Chanturija, T.A.: Oscillating and monotone solutions of first-order differential equations with deviating argument. Differentsiaµnye Uravneniya, 18, 8, 1982, 1463-1465, (in Russian). MR 0671174
[15] Koplatadze, R.G., Kvinikadze, G.: On the oscillation of solutions of first order delay differential inequalities and equations. Georgian Math. J., 1, 6, 1994, 675-685, DOI 10.1007/BF02254685 | MR 1296574
[16] Kwong, M.K.: Oscillation of first-order delay equations. J. Math. Anal. Appl., 156, 1, 1991, 274-286, DOI 10.1016/0022-247X(91)90396-H | MR 1102611
[17] Ladas, G., Lakshmikantham, V., Papadakis, L.S.: Oscillations of higher-order retarded differential equations generated by the retarded arguments. Delay and functional differential equations and their applications, 1972, 219-231, Academic Press, MR 0387776
[18] Ladde, G.S.: Oscillations caused by retarded perturbations of first order linear ordinary differential equations. Atti Acad. Naz. Lincei Rendiconti, 63, 5, 1977, 351-359, MR 0548601
[19] Ladde, G.S., Lakshmikantham, V., Zhang, B.G.: Oscillation Theory of Differential Equations with Deviating Arguments. 1987, Monographs and Textbooks in Pure and Applied Mathematics, 110, Marcel Dekker, Inc., New York, MR 1017244 | Zbl 0832.34071
[20] Li, X., Zhu, D.: Oscillation and nonoscillation of advanced differential equations with variable coefficients. J. Math. Anal. Appl., 269, 2, 2002, 462-488, DOI 10.1016/S0022-247X(02)00029-X | MR 1907126
[21] El-Morshedy, H.A., Attia, E.R.: New oscillation criterion for delay differential equations with non-monotone arguments. Appl. Math. Lett., 54, 2016, 54-59, DOI 10.1016/j.aml.2015.10.014 | MR 3434455
[22] My¹kis, A.D.: Linear homogeneous differential equations of first order with deviating arguments. Uspekhi Mat. Nauk, 5, 36, 1950, 160-162, (in Russian). MR 0036423
[23] Yu, J.S., Wang, Z.C., Zhang, B.G., Qian, X.Z.: Oscillations of differential equations with deviating arguments. Panamer. Math. J., 2, 2, 1992, 59-78, MR 1160129
[24] Zhang, B.G.: Oscillation of solutions of the first-order advanced type differential equations. Science Exploration, 2, 1982, 79-82, MR 0713776
[25] Zhou, D.: On some problems on oscillation of functional differential equations of first order. J. Shandong University, 25, 1990, 434-442,
Search
Partner of
