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Oscillation criteria for second-order quasi-linear neutral functional differential equation
| 1. | Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt |
| 2. | Department of Mathematics, Faculty of Science, Hadhramout University, Seiyun, Yemen |
In this work, new sufficient conditions for oscillation of solution of second order neutral delay differential equation are established. One objective of our paper is to further simplify and complement some results which were published lately in the literature. In order to support our results, we introduce illustrating examples.
References:
| [1] |
R. P. Agarwal, S. R. Grace and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 2000.
doi: 10.1007/978-94-015-9401-1. |
| [2] |
R. Arul and V. S. Shobha,
Oscillation of second order quasilinear differential equations with several neutral terms, J. Progressive Research in Math., (JPRM), 7 (2016), 975-981.
|
| [3] |
O. Bazighifan, E. M. Elabbasy and O. Moaaz, Oscillation of higher-order differential equations with distributed delay, J. Ineq. Appl., (2019), 9 pp.
doi: 10.1186/s13660-019-2003-0. |
| [4] |
O. Diekmann, S. A. van Gils and S. M. Verduyn Lunel, Hans-Otto Delay Equations: Functional, Complex and Nonlinear Analysis, Applied Mathematical Sciences, 110. Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4206-2. |
| [5] |
E. M. Elabbasy, T. S. Hassan and O. Moaaz,
Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Opuscula Mathematica, 32 (2012), 719-730.
doi: 10.7494/OpMath.2012.32.4.719. |
| [6] |
L. H. Erbe, Q. K. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics, 190. Marcel Dekker, Inc., New York, 1995. |
| [7] |
J. K. Hale, Functional Differential Equations, Applied Mathematical Sciences, Vol. 3. Springer-Verlag New York, New York-Heidelberg, 1971. |
| [8] |
G. S. Ladde, V. Lakshmikantham and B. G. Zhang, Oscillation Theory of Differential Eequations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics, 110. Marcel Dekker, Inc., New York, 1987. |
| [9] |
H. D. Liu, F. W. Meng and P. C. Liu,
Oscillation and asymptotic analysis on a new generalized Emden-Fowler equation, Appl. Math. Comput., 219 (2012), 2739-2748.
doi: 10.1016/j.amc.2012.08.106. |
| [10] |
J. W. Luo,
Oscillation criteria for second-order quasi-linear neutral difference equations, Comput. Math. Appl., 43 (2002), 1549-1557.
doi: 10.1016/S0898-1221(02)00118-9. |
| [11] |
O. Moaaz, E. M. Elabbasy and O. Bazighifan, On the asymptotic behavior of fourth-order functional differential equations, Adv. Difference Equ., (2017), 13 pp.
doi: 10.1186/s13662-017-1312-1. |
| [12] |
O. Moaaz, E. M. Elabbasy and E. Shaaban,
Oscillation criteria for a class of third order damped differential equations, Arab J. Math. Sci., 24 (2018), 16-30.
doi: 10.1016/j.ajmsc.2017.07.001. |
| [13] |
M. V. Ruzhansky, Y. Je Cho, P. Agarwal and I. Area, Advances in Real and Complex Analysis with Applications, Trends in Mathematics, Birkhäuser/Springer, Singapore, 2017. |
| [14] |
S. Saker, Oscillation theory of delay differential and difference equations, VDM Verlag Dr. Muller, Saarbrucken, (2010). |
| [15] |
H. L. Smith, Monotone Dynamical System: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995. |
| [16] |
I. P. Stavroulakis,
Nonlinear delay differential inequalities, Nonlinear Anal., 6 (1982), 389-396.
doi: 10.1016/0362-546X(82)90024-4. |
| [17] |
S. R. Sun, T. X. Li, Z. L. Han and C. Zhang,
On oscillation of second-order nonlinear neutral functional differential equations, Bull. Malays. Math. Sci. Soc. (2), 36 (2013), 541-554.
|
| [18] |
X. H. Tang,
Oscillation for first order superlinear delay differential equations, J. London Math. Soc. (2), 65 (2002), 115-122.
doi: 10.1112/S0024610701002678. |
| [19] |
X. L. Wang and F. W. Meng,
Oscillation criteria of second-order quasi-linear neutral delay differential equations, Math. Comput. Model., 46 (2007), 415-421.
doi: 10.1016/j.mcm.2006.11.014. |
| [20] |
Y. Z. Wu, Y. H. Yu, J. M. Zhang and J. S. Xiao, Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type, J. Inequal. Appl., 2016 (2016), 11 pp.
doi: 10.1186/s13660-016-1268-9. |
| [21] |
H. Yaldız and P. Agarwal,
$S$-convex functions on discrete time domains, Analysis, 37 (2017), 179-184.
doi: 10.1515/anly-2017-0015. |
show all references
References:
| [1] |
R. P. Agarwal, S. R. Grace and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 2000.
doi: 10.1007/978-94-015-9401-1. |
| [2] |
R. Arul and V. S. Shobha,
Oscillation of second order quasilinear differential equations with several neutral terms, J. Progressive Research in Math., (JPRM), 7 (2016), 975-981.
|
| [3] |
O. Bazighifan, E. M. Elabbasy and O. Moaaz, Oscillation of higher-order differential equations with distributed delay, J. Ineq. Appl., (2019), 9 pp.
doi: 10.1186/s13660-019-2003-0. |
| [4] |
O. Diekmann, S. A. van Gils and S. M. Verduyn Lunel, Hans-Otto Delay Equations: Functional, Complex and Nonlinear Analysis, Applied Mathematical Sciences, 110. Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4206-2. |
| [5] |
E. M. Elabbasy, T. S. Hassan and O. Moaaz,
Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Opuscula Mathematica, 32 (2012), 719-730.
doi: 10.7494/OpMath.2012.32.4.719. |
| [6] |
L. H. Erbe, Q. K. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics, 190. Marcel Dekker, Inc., New York, 1995. |
| [7] |
J. K. Hale, Functional Differential Equations, Applied Mathematical Sciences, Vol. 3. Springer-Verlag New York, New York-Heidelberg, 1971. |
| [8] |
G. S. Ladde, V. Lakshmikantham and B. G. Zhang, Oscillation Theory of Differential Eequations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics, 110. Marcel Dekker, Inc., New York, 1987. |
| [9] |
H. D. Liu, F. W. Meng and P. C. Liu,
Oscillation and asymptotic analysis on a new generalized Emden-Fowler equation, Appl. Math. Comput., 219 (2012), 2739-2748.
doi: 10.1016/j.amc.2012.08.106. |
| [10] |
J. W. Luo,
Oscillation criteria for second-order quasi-linear neutral difference equations, Comput. Math. Appl., 43 (2002), 1549-1557.
doi: 10.1016/S0898-1221(02)00118-9. |
| [11] |
O. Moaaz, E. M. Elabbasy and O. Bazighifan, On the asymptotic behavior of fourth-order functional differential equations, Adv. Difference Equ., (2017), 13 pp.
doi: 10.1186/s13662-017-1312-1. |
| [12] |
O. Moaaz, E. M. Elabbasy and E. Shaaban,
Oscillation criteria for a class of third order damped differential equations, Arab J. Math. Sci., 24 (2018), 16-30.
doi: 10.1016/j.ajmsc.2017.07.001. |
| [13] |
M. V. Ruzhansky, Y. Je Cho, P. Agarwal and I. Area, Advances in Real and Complex Analysis with Applications, Trends in Mathematics, Birkhäuser/Springer, Singapore, 2017. |
| [14] |
S. Saker, Oscillation theory of delay differential and difference equations, VDM Verlag Dr. Muller, Saarbrucken, (2010). |
| [15] |
H. L. Smith, Monotone Dynamical System: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995. |
| [16] |
I. P. Stavroulakis,
Nonlinear delay differential inequalities, Nonlinear Anal., 6 (1982), 389-396.
doi: 10.1016/0362-546X(82)90024-4. |
| [17] |
S. R. Sun, T. X. Li, Z. L. Han and C. Zhang,
On oscillation of second-order nonlinear neutral functional differential equations, Bull. Malays. Math. Sci. Soc. (2), 36 (2013), 541-554.
|
| [18] |
X. H. Tang,
Oscillation for first order superlinear delay differential equations, J. London Math. Soc. (2), 65 (2002), 115-122.
doi: 10.1112/S0024610701002678. |
| [19] |
X. L. Wang and F. W. Meng,
Oscillation criteria of second-order quasi-linear neutral delay differential equations, Math. Comput. Model., 46 (2007), 415-421.
doi: 10.1016/j.mcm.2006.11.014. |
| [20] |
Y. Z. Wu, Y. H. Yu, J. M. Zhang and J. S. Xiao, Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type, J. Inequal. Appl., 2016 (2016), 11 pp.
doi: 10.1186/s13660-016-1268-9. |
| [21] |
H. Yaldız and P. Agarwal,
$S$-convex functions on discrete time domains, Analysis, 37 (2017), 179-184.
doi: 10.1515/anly-2017-0015. |
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