Oscillation criteria for sublinear and superlinear first-order difference equations of neutral type with several delays

Mohamed Altanji; Gokula Nanda Chhatria; Shyam Sundar Santra; Andrea Scapellato; Mohamed Altanji; Gokula Nanda Chhatria; Shyam Sundar Santra; Andrea Scapellato

doi:10.3934/math.2022973

AIMS Mathematics

2022, Volume 7, Issue 10: 17670-17684. doi: 10.3934/math.2022973

Previous Article Next Article

Research article

Oscillation criteria for sublinear and superlinear first-order difference equations of neutral type with several delays

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2.
Department of Mathematics, Sambalpur University, Sambalpur 768019, India
3.
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
4.
Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies (UPES), Dehradun, Uttarakhand 248007, India
5.
Department of Mathematics and Computer Science, University of Catania, Catania 95125, Italy

Received: 02 February 2022 Revised: 17 June 2022 Accepted: 18 June 2022 Published: 01 August 2022
MSC : 34C10, 39A10, 39A12, 39A21

The purpose of this paper is to investigate the oscillatory behaviour of a class of first-order sublinear and superlinear neutral difference equations. Some conditions are established by applying Banach's Contraction mapping principle, Knaster-Tarski fixed point theorem and using several inequalities. We provide some examples to illustrate the outreach of the main results.
- difference equation,
- oscillation,
- neutral,
- fixed point theorem,
- sublinear,
- superlinear
Citation: Mohamed Altanji, Gokula Nanda Chhatria, Shyam Sundar Santra, Andrea Scapellato. Oscillation criteria for sublinear and superlinear first-order difference equations of neutral type with several delays[J]. AIMS Mathematics, 2022, 7(10): 17670-17684. doi: 10.3934/math.2022973

Related Papers:

Abstract

The purpose of this paper is to investigate the oscillatory behaviour of a class of first-order sublinear and superlinear neutral difference equations. Some conditions are established by applying Banach's Contraction mapping principle, Knaster-Tarski fixed point theorem and using several inequalities. We provide some examples to illustrate the outreach of the main results.

References

[1]	R. P. Agarwal, Difference equations and inequalities: Theory, methods, and applications, Marcel Dekker, New York, 2000.
[2]	R. P. Agarwal, M. Bohner, S. R. Grace, D. O'Regan, Discrete oscillation theory, Hindawi Publishing Corporation, New York, 2005.
[3]	T. Candan, Existence of nonoscillatory solutions to first order neutral differential equations, Electon. J. Differ. Equ., 2016 (2016), 1–11.
[4]	G. E. Chatzarakis, G. N. Miliaras, Asymptotic behaviour in neutral difference equations with variable coefficients and more than one day arguments, J. Math. Comput. Sci., 1 (2012), 32–52.
[5]	L. H. Erbe, Q. Kong, B. G. Zhang, Oscillation theory for functional differential equations, Marcel Dekker Inc., New York, 1995.
[6]	Y. Gao, G. Zhang, Oscillation of nonlinear first order neutral difference equations, Appl. Math. E-Notes, 1 (2001), 5–10.
[7]	D. A. Georgiou, E. A Grove, G. Ladas, Oscillations of neutral difference equations, Appl. Anal., 33 (1989), 243–253. https://doi.org/10.1080/00036818908839876 doi: 10.1080/00036818908839876
[8]	G. Gomathi Jawahar, Oscillation properties of certain types of first order neutral delay difference equations, Int. J. Sci. Eng. Res., 4 (2013), 1197–1201.
[9]	I. Györi, G. Ladas, Oscillation theory of delay differential equations with applications, Clarendon Press, Oxford, 1991.
[10]	J. R. Graef, E. Thandapani, S. Elizabeth, Oscillation of first order nonlinear neutral difference equations, Indian J. Pure Appl. Math., 36 (2005), 503–512.
[11]	B. Karpuz, Sharp conditions for oscillation and nonoscillation of neutral difference equations, In: M. Bohner, S. Siegmund, R. Simon Hilscher, P. Stehlik, Difference equations and discrete dynamical systems with applications, ICDEA 2018, Springer Proceedings in Mathematics & Statistics, Vol. 312, Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-35502-9_11
[12]	V. Kolmanovski, A. Myshkis, Introduction to the theory and applications of functional differential equations, Kluwer, Dordrecht, 1999.
[13]	F. Kong, Existence of nonoscillatory solutions of a kind of first order neutral differential equation, Math. Commun., 22 (2017), 151–164.
[14]	X. Lin, Oscillation of solutions of neutral difference equations with a nonlinear neutral term, Comput. Math. Appl., 52 (2006), 439–448. https://doi.org/10.1016/j.camwa.2006.02.009 doi: 10.1016/j.camwa.2006.02.009
[15]	Q. Li, C. Wang, F. Li, H. Liang, Z. Zhang, Oscillation of sublinear difference equations with positive neutral term, J. Appl. Math. Comput., 20 (2006), 305–314. https://doi.org/10.1007/BF02831940 doi: 10.1007/BF02831940
[16]	A. Murugesan, R. Suganthi, Oscillation behaviour of first order nonlinear functional neutral delay difference equations, Int. J. Differ. Equ., 12 (2017), 1–13.
[17]	A. D. Myschkis, Lineare Differentialgleichungen mit nacheilendem Argument, VEB Deutscher Verlag der Wissenschaften, Berlin, 1955.
[18]	S. S. Santra, D. Baleanu, K. M. Khedher, O. Moaaz, First-order impulsive differential systems: Sufficient and necessary conditions for oscillatory or asymptotic behavior, Adv. Differ. Equ., 2021 (2021), 283 https://doi.org/10.1186/s13662-021-03446-1 doi: 10.1186/s13662-021-03446-1
[19]	O. Öcalan, Oscillation criteria for systems of difference equations with variable coefficients, Appl. Math. E-Notes, 6 (2006), 119–125.
[20]	O. Öcalan, O. Duman, Oscillation analysis of neutral difference equations with delays, Chaos, Solitons, Fract., 39 (2009), 261–270. https://doi.org/10.1016/j.chaos.2007.01.094 doi: 10.1016/j.chaos.2007.01.094
[21]	O. Öcalan, Linearized oscillation of nonlinear difference equation with advanced arguments, Arch. Math. (Brno), 45 (2009), 203–212.
[22]	N. Parhi, A. K. Tripathy, Oscillation of forced nonlinear neutral delay difference equations of first order, Czech. Math. J., 53 (2003), 83–101.
[23]	N. Parhi, A. K. Tripathy, Oscillation of a class neutral difference equations of higher order, J. Math. Anal. Appl., 28 (2003), 756–774. https://doi.org/10.1016/S0022-247X(03)00298-1 doi: 10.1016/S0022-247X(03)00298-1
[24]	H. Péics, Positive solutions of neutral delay difference equations, Novi. Sad. J. Math., 35 (2005), 111–122.
[25]	S. H. Saker, M. A. Arahet, New oscillation criteria of first order neutral delay difference equations of Emden-Fowler type, J. Comput. Anal. Appl., 29 (2021), 252–265.
[26]	S. S. Santra, D. Majumder, R. Bhattacharjee, T. Ghosh, Asymptotic behaviour for first-order difference equations I, In: Applications of networks, sensors and autonomous systems analytics, Studies in Autonomic, Data-driven and Industrial Computing, Singapore: Springer, 2022. https://doi.org/10.1007/978-981-16-7305-4_4
[27]	X. H. Tang, X. Lin, Necessary and sufficient conditions for oscillation of first-order nonlinear neutral difference equations, Comput. Math. Appl., 55 (2008), 1279–1292. https://doi.org/10.1016/j.camwa.2007.06.009 doi: 10.1016/j.camwa.2007.06.009
[28]	M. K. Yildiz, H. Öğünmez, Oscillatory results of higher order nonlinear neutral delay difference equations with a nonlinear neutral term, Hacet. J. Math. Stat., 43 (2014), 809–814.
[29]	G. Zhang, Oscillation for nonlinear neutral difference equations, Appl. Math. E-Notes, 2 (2002), 22–24.

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)