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

Abstract

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Sufficient oscillation conditions involving lim sup and lim inf 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.

How to cite

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Chatzarakis, 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

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  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, (2016) MR3479781
  2. 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
  3. Chatzarakis, G.E., Differential equations with non-monotone arguments: Iterative Oscillation results, J. Math. Comput. Sci., 6, 5, 2016, 953-964, (2016) 
  4. Chatzarakis, G.E., 10.1007/s00009-017-0883-0, Mediterr. J. Math., 14, 2, 2017, 82, (2017) MR3620160DOI10.1007/s00009-017-0883-0
  5. 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
  6. Chatzarakis, G.E., Li, T., 10.1155/2018/8237634, Complexity, 2018, 2018, 1-18, Article ID 8237634.. (2018) MR3620160DOI10.1155/2018/8237634
  7. Chatzarakis, G.E., Öcalan, Ö., 10.1080/14689367.2015.1036007, Dynamical Systems, 30, 3, 2015, 310-323, (2015) MR3373715DOI10.1080/14689367.2015.1036007
  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, (1995) MR1309905
  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, (1988) MR0929918
  10. Fukagai, N., Kusano, T., 10.1007/BF01773379, Ann. Mat. Pura Appl., 136, 1, 1984, 95-117, (1984) Zbl0552.34062MR0765918DOI10.1007/BF01773379
  11. Jaro¹, J., Stavroulakis, I.P., 10.1216/rmjm/1181071686, Rocky Mountain J. Math., 29, 1, 1999, 197-207, (1999) MR1687662DOI10.1216/rmjm/1181071686
  12. Jian, C., On the oscillation of linear differential equations with deviating arguments, Math. in Practice and Theory, 1, 1, 1991, 32-40, (1991) MR1107456
  13. 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
  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). (1982) MR0671174
  15. Koplatadze, R.G., Kvinikadze, G., 10.1007/BF02254685, Georgian Math. J., 1, 6, 1994, 675-685, (1994) MR1296574DOI10.1007/BF02254685
  16. 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
  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, (1972) MR0387776
  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, (1977) MR0548601
  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, (1987) Zbl0832.34071MR1017244
  20. 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
  21. 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
  22. 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
  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, (1992) MR1160129
  24. Zhang, B.G., Oscillation of solutions of the first-order advanced type differential equations, Science Exploration, 2, 1982, 79-82, (1982) MR0713776
  25. Zhou, D., On some problems on oscillation of functional differential equations of first order, J. Shandong University, 25, 1990, 434-442, (1990) 

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