New results on the oscillation of second-order damped neutral differential equations with several sub-linear neutral terms
Volume 34, Issue 2, pp 191--204
https://dx.doi.org/10.22436/jmcs.034.02.08
Publication Date: March 07, 2024
Submission Date: September 17, 2023
Revision Date: November 27, 2023
Accteptance Date: January 29, 2024
Authors
A. A. El-Gaber
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt.
E. I. El-Saedy
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt.
M. M. A. El-Sheikh
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt.
S. A. A. El-Marouf
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt.
- Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia.
Abstract
In this paper, we establish some new sufficient conditions which guarantee
the oscillatory behavior of solutions of a class of second-order damped
neutral differential equations with sub-linear neutral terms. Our criteria
improve and complement related results in the literature. Two examples are
given to justify our main results.
Share and Cite
ISRP Style
A. A. El-Gaber, E. I. El-Saedy, M. M. A. El-Sheikh, S. A. A. El-Marouf, New results on the oscillation of second-order damped neutral differential equations with several sub-linear neutral terms, Journal of Mathematics and Computer Science, 34 (2024), no. 2, 191--204
AMA Style
El-Gaber A. A., El-Saedy E. I., El-Sheikh M. M. A., El-Marouf S. A. A., New results on the oscillation of second-order damped neutral differential equations with several sub-linear neutral terms. J Math Comput SCI-JM. (2024); 34(2):191--204
Chicago/Turabian Style
El-Gaber, A. A., El-Saedy, E. I., El-Sheikh, M. M. A., El-Marouf, S. A. A.. "New results on the oscillation of second-order damped neutral differential equations with several sub-linear neutral terms." Journal of Mathematics and Computer Science, 34, no. 2 (2024): 191--204
Keywords
- Oscillation
- second order damped differential equations
- neutral differential equations
- sub-linear neutral terms
MSC
References
-
[1]
R. P. Agarwal, M. Bohner, T. Li, Oscillatory behavior of second-order half-linear damped dynamic equations, Appl. Math. Comput., 254 (2015), 408–418
-
[2]
R. P. Agarwal, M. Bohner, T. Li, C. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math., 30 (2014), 1–6
-
[3]
R. P. Agarwal, C. Zhang, T. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput., 274 (2016), 178–181
-
[4]
B. Bacul´ıkov´, Oscillatory criteria for second order differential equations with several sublinear neutral terms, Opuscula Math., 39 (2019), 753–763
-
[5]
B. Bacul´ıkov´a, J. Dˇzurina, Oscillation theorems for second-order nonlinear neutral differential equations, Comput. Math. Appl., 62 (2011), 4472–4478
-
[6]
X. Beqiri, E. Koci, Oscillation criteria for second order nonlinear differential equations, British J. Sci., 6 (2012), 73–80
-
[7]
M. Bohner, T. Li, Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient, Appl. Math. Lett., 37 (2014), 72–76
-
[8]
M. Bohner, T. Li, Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math., 58 (2015), 1445–1452
-
[9]
D. C¸ akmak, Oscillation for second order nonlinear differential equations with damping, Dynam. Systems Appl., 17 (2008), 139–147
-
[10]
C. Dharuman, N. Prabaharan, E. Thandapani, E. Tunc, Modified oscillation results for second-order nonlinear differential equations with sublinear neutral terms, Appl. Math. E-Notes, 22 (2022), 299–309
-
[11]
J. Dˇzurina, S. R. Grace, I. Jadlovsk´a, T. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293 (2020), 910–992
-
[12]
J. Dˇzurina, E. Thandapani, B. Bacul´ıkov´a, C. Dharuman, N. Prabaharan, Oscillation of second order Nonlinear Differential Equations with several sub-linear neutral terms, Nonlinear Dyn. Syst. Theory, 19 (2019), 124–132
-
[13]
M. M. A. El-Sheikh, Oscillation and nonoscillation criteria for second order nonlinear differential equations. I, J. Math. Anal. Appl., 179 (1993), 14–27
-
[14]
M. M. A. El-Sheikh, R. A. Sallam, D. I. Elimy, Oscillation criteria for second order nonlinear equations with damping, Adv. Differ. Equ. Control Process., 8 (2011), 127–142
-
[15]
X. Fu, T. Li, Ch. Zhang, Oscillation of second-order damped differential equations, Adv. Difference Equ., 2013 (2013), 11 pages
-
[16]
S. R. Grace, I. Jadlovsk´, Oscillation criteria for second-order neutral damped differential equations with delay arguments, In: Dynamical Systems—Analytical and Computational Techniques, INTECH, chap. 2, (2017), 31–53
-
[17]
S. R. Grace, B. S. Lalli, Oscillation of nonlinear second order neutral differential equations, Rad. Mat., 3 (1987), 77–84
-
[18]
M. K. Grammatikopoulos, G. Ladas, A. Meimaridou, Oscillation of second order neutral delay differential equations, Rad. Mat., 1 (1985), 267–274
-
[19]
J. Hale, Functional differential equations, Springer, Berlin-New York (1971)
-
[20]
J. Hale, Theory of functional differential equations, Springer-Verlag, New York-Heidelberg (1977)
-
[21]
I. Jadlovsk´a, Oscillation criteria of Kenser-type for second-order half-linear advanced differential equations, Appl. Math. Lett., 106 (2020), 1–8
-
[22]
I. Jodlovsk´, New criteria for sharp oscillation of second-order neutral delay differential equations, Mathematics, 9 (2021), 1–23
-
[23]
T. Li, S. Frassu, G. Viglialora, Combining effects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys., 74 (2023), 21 pages
-
[24]
T. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 18 pages
-
[25]
T. Li, Y. V. Rogovchenko, Asymptotic behavior of an odd-order delay differential equation, Bound. Value Probl., 2014 (2014), 10 pages
-
[26]
T. Li, Y. V. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr., 288 (2015), 1150–1162
-
[27]
T. Li, Y. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett., 61 (2016), 35–41
-
[28]
T. Li, Y. V. Rogovchenko, On asymptotic behavior of solutions to higher-order sublinear Emden-Fowler delay differential equations, Appl. Math. Lett., 67 (2017), 53–59
-
[29]
T. Li, Y. V. Rogovchenko, Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math., 184 (2017), 489–500
-
[30]
T. Li, Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), 7 pages
-
[31]
T. Li, Y. V. Rogovchenko, S. Tang, Oscillation of second-order nonlinear differential equations with damping, Math. Slovaca, 64 (2014), 1227–1236
-
[32]
T. Li, Y. V. Rogovchenko, C. Zhang, Oscillation of second-order neutral differential equations, Funkcial. Ekvac., 56 (2013), 111–120
-
[33]
T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differential Integral Equations, 34 (2021), 315–336
-
[34]
H. Liu, F. Meng, P. Liu, Oscillation and asymptotic analysis on a new generalized Emden-Fowler equation, Appl. Math. Comput., 219 (2012), 2739–2748
-
[35]
Y. V. Rogovchenko, Oscillation theorems for second-order equations with damping, Nonlinear Anal., 41 (2000), 1005– 1028
-
[36]
Y. V. Rogovchenko, F. Tuncay, Interval oscillation criteria for second order nonlinear differential equations with damping, Dynam. Systems Appl., 16 (2007), 337–344
-
[37]
Y. V. Rogovchenko, F. Tuncay, Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal., 69 (2008), 208–221
-
[38]
R. A. Sallam, M. M. A. El-Sheikh, E. I. El-Saedy, On the oscillation of second order nonlinear neutral delay differential equations, Math. Slovaca, 71 (2021), 859–870
-
[39]
A. A. Soliman, R. A. Sallam, A. M. Hassan, Oscillation criteria of second order nonlinear neutral differential equations, Int. J. Appl. Math. Res., 1 (2012), 314–322
-
[40]
R.Wang, Q. Li, Oscillation and asymptotic properties of a class of second-order Emden-Fowler neutral differential equations, SpringerPlus, 5 (2016), 1–15
-
[41]
Y. Wu, Y. Yu, J. Xiao, Oscillation of second order nonlinear neutral differential equations, Mathematics, 10 (2022), 1–12
-
[42]
Y. Wu, Y. Yu, J. Zhang, J. Xiao, Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type, J. Inequal. Appl., 2016 (2016), 11 pages
