# Oscillation in deviating differential equations using an iterative method

George E. Chatzarakis; Irena Jadlovská

Communications in Mathematics (2019)

- Volume: 27, Issue: 2, page 143-169
- ISSN: 1804-1388

## Access Full Article

top## Abstract

top## How to cite

topChatzarakis, George E., and Jadlovská, Irena. "Oscillation in deviating differential equations using an iterative method." Communications in Mathematics 27.2 (2019): 143-169. <http://eudml.org/doc/295029>.

@article{Chatzarakis2019,

abstract = {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.},

author = {Chatzarakis, George E., Jadlovská, Irena},

journal = {Communications in Mathematics},

keywords = {differential equation; non-monotone argument; oscillatory solution; nonoscillatory solution; Grönwall inequality},

language = {eng},

number = {2},

pages = {143-169},

publisher = {University of Ostrava},

title = {Oscillation in deviating differential equations using an iterative method},

url = {http://eudml.org/doc/295029},

volume = {27},

year = {2019},

}

TY - JOUR

AU - Chatzarakis, George E.

AU - Jadlovská, Irena

TI - Oscillation in deviating differential equations using an iterative method

JO - Communications in Mathematics

PY - 2019

PB - University of Ostrava

VL - 27

IS - 2

SP - 143

EP - 169

AB - 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.

LA - eng

KW - differential equation; non-monotone argument; oscillatory solution; nonoscillatory solution; Grönwall inequality

UR - http://eudml.org/doc/295029

ER -

## References

top- Braverman, E., Chatzarakis, G.E., Stavroulakis, I.P., Iterative oscillation tests for differential equations with several non-monotone arguments, Adv. Difference Equ., 87, 2016, (2016) MR3479781
- Braverman, E., Karpuz, B., On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput., 218, 7, 2011, 3880-3887, (2011) MR2851485
- Chatzarakis, G.E., Differential equations with non-monotone arguments: Iterative Oscillation results, J. Math. Comput. Sci., 6, 5, 2016, 953-964, (2016)
- Chatzarakis, G.E., 10.1007/s00009-017-0883-0, Mediterr. J. Math., 14, 2, 2017, 82, (2017) MR3620160DOI10.1007/s00009-017-0883-0
- Chatzarakis, G.E., Jadlovská, I., 10.7494/OpMath.2018.38.3.327, Opuscula Math., 38, 3, 2018, 327-356, (2018) MR3781617DOI10.7494/OpMath.2018.38.3.327
- Chatzarakis, G.E., Li, T., 10.1155/2018/8237634, Complexity, 2018, 2018, 1-18, Article ID 8237634.. (2018) MR3620160DOI10.1155/2018/8237634
- Chatzarakis, G.E., Öcalan, Ö., 10.1080/14689367.2015.1036007, Dynamical Systems, 30, 3, 2015, 310-323, (2015) MR3373715DOI10.1080/14689367.2015.1036007
- 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, (1995) MR1309905
- Erbe, L.H., Zhang, B.G., Oscillation of first order linear differential equations with deviating arguments, Differential Integral Equations, 1, 3, 1988, 305-314, (1988) MR0929918
- Fukagai, N., Kusano, T., 10.1007/BF01773379, Ann. Mat. Pura Appl., 136, 1, 1984, 95-117, (1984) Zbl0552.34062MR0765918DOI10.1007/BF01773379
- Jaro¹, J., Stavroulakis, I.P., 10.1216/rmjm/1181071686, Rocky Mountain J. Math., 29, 1, 1999, 197-207, (1999) MR1687662DOI10.1216/rmjm/1181071686
- Jian, C., On the oscillation of linear differential equations with deviating arguments, Math. in Practice and Theory, 1, 1, 1991, 32-40, (1991) MR1107456
- Kon, M., Sficas, Y.G., Stavroulakis, I.P., 10.1090/S0002-9939-00-05530-1, Proc. Amer. Math. Soc., 128, 10, 2000, 2989-2998, (2000) MR1694869DOI10.1090/S0002-9939-00-05530-1
- 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). (1982) MR0671174
- Koplatadze, R.G., Kvinikadze, G., 10.1007/BF02254685, Georgian Math. J., 1, 6, 1994, 675-685, (1994) MR1296574DOI10.1007/BF02254685
- Kwong, M.K., 10.1016/0022-247X(91)90396-H, J. Math. Anal. Appl., 156, 1, 1991, 274-286, (1991) MR1102611DOI10.1016/0022-247X(91)90396-H
- 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, (1972) MR0387776
- 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, (1977) MR0548601
- 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, (1987) Zbl0832.34071MR1017244
- Li, X., Zhu, D., 10.1016/S0022-247X(02)00029-X, J. Math. Anal. Appl., 269, 2, 2002, 462-488, (2002) MR1907126DOI10.1016/S0022-247X(02)00029-X
- El-Morshedy, H.A., Attia, E.R., 10.1016/j.aml.2015.10.014, Appl. Math. Lett., 54, 2016, 54-59, (2016) MR3434455DOI10.1016/j.aml.2015.10.014
- My¹kis, A.D., Linear homogeneous differential equations of first order with deviating arguments, Uspekhi Mat. Nauk, 5, 36, 1950, 160-162, (in Russian). (1950) MR0036423
- 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, (1992) MR1160129
- Zhang, B.G., Oscillation of solutions of the first-order advanced type differential equations, Science Exploration, 2, 1982, 79-82, (1982) MR0713776
- Zhou, D., On some problems on oscillation of functional differential equations of first order, J. Shandong University, 25, 1990, 434-442, (1990)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.