×

zbMATH — the first resource for mathematics

On oscillation of differential equations with non-monotone deviating arguments. (English) Zbl 1369.34088
Summary: In this paper, we present sufficient conditions involving limsup which guarantee the oscillation of all solutions of a differential equation with non-monotone deviating argument and non-negative coefficients. Corresponding differential equations of both delayed and advanced type are studied. Using algorithms on MATLAB software, examples are given to demonstrate the advantage of our results.

MSC:
34K11 Oscillation theory of functional-differential equations
34K06 Linear functional-differential equations
Software:
Matlab
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agarwal, R.P., Berezansky, L., Braverman, E., Domoshnitsky, A.: Nonoscillation Theory of Functional Differential Equations with Applications. Springer, New York (2012) · Zbl 1253.34002
[2] Akca, H; Chatzarakis, GE; Stavroulakis, IP, An oscillation criterion for delay differential equations with several non-monotone arguments, Appl. Math. Lett., 59, 101-108, (2016) · Zbl 1341.34070
[3] Babakhani, A., Baleanu, D.: Existence of positive solutions for a class of delay fractional differential equations with generalization to \(N\)-term. Abstract Appl. Anal. (2011) (article ID 391971, 14 pages) · Zbl 1217.34007
[4] Braverman, E., Chatzarakis, G.E., Stavroulakis, I.P.: Iterative oscillation tests for differential equations with several non-monotone arguments. Adv. Differ. Equ. (2016). doi:10.1186/s13662-016-0817-3 · Zbl 1348.34121
[5] Braverman, E; Karpuz, B, On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput., 218, 3880-3887, (2011) · Zbl 1256.39013
[6] Chatzarakis, GE, Differential equations with non-monotone arguments: iterative oscillation results, J. Math. Comput. Sci., 6, 953-964, (2016)
[7] Chatzarakis, G.E., Öcalan, Ö.: Oscillations of differential equations with several non-monotone advanced arguments. Dyn. Syst. Int. J. (2015). doi:10.1080/14689367.2015.1036007 · Zbl 1330.34107
[8] El-Morshedy, HA; Attia, ER, New oscillation criterion for delay differential equations with non-monotone arguments, Appl. Math. Lett., 54, 54-59, (2016) · Zbl 1331.34132
[9] Doha, E.H., Baleanu, D., Bhrawy, A.H., Hafez, R.M.: A pseudospectral algorithm for solving multipantograph delay systems on a semi-infinite interval using Legendre rational functions. Abstract Appl. Anal. (2014) (article ID 816473, 9 pages)
[10] Erbe, L.H., Kong, Q., Zhang, B.G.: Oscillation Theory for Functional Differential Equations. Marcel Dekker, New York (1995) · Zbl 0821.34067
[11] Erbe, LH; Zhang, BG, Oscillation of first order linear differential equations with deviating arguments, Differ. Integral Equ., 1, 305-314, (1988) · Zbl 0723.34055
[12] Fukagai, N; Kusano, T, Oscillation theory of first order functional-differential equations with deviating arguments, Ann. Mat. Pura Appl., 136, 95-117, (1984) · Zbl 0552.34062
[13] Hunt, BR; Yorke, JA, When all solutions of \(x^{{′ }}\left( t \right)=-\mathop ∑ \nolimits ^ q_i \left( t \right)x(t-T_i \left( t \right))\) oscillate, J. Differ. Equ., 53, 139-145, (1984) · Zbl 0571.34057
[14] Jaroš, J; Stavroulakis, IP, Oscillation tests for delay equations, Rocky Mt. J. Math., 45, 2989-2997, (2000) · Zbl 0951.34045
[15] Jian, C, On the oscillation of linear differential equations with deviating arguments, Math. Pract. Theory, 1, 32-40, (1991)
[16] Kon, M; Sficas, YG; Stavroulakis, IP, Oscillation criteria for delay equations, Proc. Am. Math. Soc., 128, 675-685, (1994) · Zbl 0951.34045
[17] Koplatadze, R.G., Chanturija, T.A.: Oscillating and monotone solutions of first-order differential equations with deviating argument (Russian). Differ. Uravn. 18, 1463-1465, 1472 (1982)
[18] Koplatadze, RG; Kvinikadze, G, On the oscillation of solutions of first order delay differential inequalities and equations, Georgian Math. J., 3, 675-685, (1994) · Zbl 0810.34068
[19] Kusano, T, On even-order functional-differential equations with advanced and retarded arguments, J. Differ. Equ., 45, 75-84, (1982) · Zbl 0512.34059
[20] Kwong, MK, Oscillation of first-order delay equations, J. Math. Anal. Appl., 156, 274-286, (1991) · Zbl 0727.34064
[21] Ladas, G., Lakshmikantham, V., Papadakis, L.S.: Delay and Functional Differential Equations and Their Applications. Oscillations of higher-order retarded differential equations generated by the retarded arguments. Academic Press, New York (1972) · Zbl 0273.34052
[22] Ladas, G; Stavroulakis, IP, Oscillations caused by several retarded and advanced arguments, J. Differ. Equ., 44, 134-152, (1982) · Zbl 0452.34058
[23] Ladde, GS, Oscillations caused by retarded perturbations of first order linear ordinary differential equations, Atti Acad. Naz. Lincei Rend., 63, 351-359, (1978) · Zbl 0402.34058
[24] Ladde, G.S., Lakshmikantham, V., Zhang, B.G.: Monographs and Textbooks in Pure and Applied Mathematics. Oscillation theory of differential equations with deviating arguments, vol. 110. Marcel Dekker, New York (1987)
[25] Li, X; Zhu, D, Oscillation and nonoscillation of advanced differential equations with variable coefficients, J. Math. Anal. Appl., 269, 462-488, (2002) · Zbl 1013.34067
[26] Myshkis, AD, Linear homogeneous differential equations of first order with deviating arguments, Uspekhi Mat. Nauk., 5, 160-162, (1950) · Zbl 0041.42108
[27] Onose, H, Oscillatory properties of the first-order differential inequalities with deviating argument, Funkc. Ekvac., 26, 189-195, (1983) · Zbl 0525.34051
[28] Stavroulakis, IP, Oscillation criteria for delay and difference equations with non-monotone arguments, Appl. Math. Comput., 226, 661-672, (2014) · Zbl 1354.34120
[29] Tang, XH, Oscillation of first order delay differential equations with distributed delay, J. Math. Anal. Appl., 289, 367-378, (2004) · Zbl 1055.34129
[30] Yu, JS; Wang, ZC; Zhang, BG; Qian, XZ, Oscillations of differential equations with deviating arguments, Panam. Math. J., 2, 59-78, (1992) · Zbl 0845.34082
[31] Zhang, BG, Oscillation of solutions of the first-order advanced type differential equations, Sci. Explor., 2, 79-82, (1982)
[32] Zhou, D, On some problems on oscillation of functional differential equations of first order, J. Shandong Univ., 25, 434-442, (1990) · Zbl 0726.34060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.