On Oscillatory Solutions of Neutral Functional Differential Equations

Main Article Content

Fatima N. Ahmed
Souad A. Abumaryam
Ioannis P. Stavroulakis

Abstract

In this article, a specific neutral functional differential equations class is considered. Some new sufficient conditions related to the oscillatory solutions are constructed. These conditions extend and improve several well-known conditions in many existing studies.

Article Details

How to Cite
Ahmed, F. N., Souad A. Abumaryam, & Stavroulakis, I. P. (2025). On Oscillatory Solutions of Neutral Functional Differential Equations. Sebha University Conference Proceedings, 4(3), 225–227. https://doi.org/10.51984/sucp.v4i3.3880
Section
Confrence Proceeding

References

Agarwal, R. P., Bohner, M. & Li, W. T. 2004. Nonoscillation and oscillation: Theory for functional differential equations. New York :Marcel Dekker.

Ahmed, F. N., Ahmad, R. R., Din, U. K. S. & Noorani, M. S. M. 2014. Some further results on oscillations for neutral delay differential equations with variable coefficients. Abstract and Applied Analysis, Vol. 2014, Article ID 579023, 6 pages.

Ahmed, F. N., Ahmad, R. R., Din, U. K. S. & Noorani, M. S. M. 2014. Oscillations for Nonlinear Neutral Delay Differential Equations with Variable Coefficients. Abstract and Applied Analysis, Vol. 2014, Article ID 179195, 6 pages.

Ahmed, F. N., Ahmad, R. R., Din, U. K. S. & Noorani, M. S. M. 2015. Oscillation criteria for nonlinear functional differential equations of neutral type. J. of Inequalities and Applications. DOI 10.1186/s13660-015-0608-5, 2015:97.

Ahmed, F. N., Ahmad, R. R., Din, U. K. S. & Noorani, M. S. M. 2018. Some open problems in the theory for neutral delay differential equations, Scientific Journal of Applied Sciences. 8: 12-18.

Chen, M. –P., Yu, J. S. & Huang, L. H. 1994. Oscillations of first order neutral differential equations with variable coefficients. J. of Math. Anal. Appl. 185:288-301.

Chuanxi, Q. & Ladas, G. 1989. Oscillations of neutral differential equations with variable

coefficients. Appl. Anal. 32: 215-228.

Chuanxi, Q., Ladas, G., Zhang B. G. & Zhao, T. 1990. Sufficient conditions for oscillation and existence of positive solutions, Appl. Anal. 35: 187-194.

Driver, R. D. 1984. A mixed neutral system. Nonlinear Analysis. 8: 155-158.

Elabbasy, E. M., Hassan T. S. & Saker, S. H. 2005. Necessary and sufficient condition for oscillations of neutral differential equation. Serdica Math. J. 31: 279-290.

Farrell, K., Grove, E. A. & Ladas, G. 1988. Neutral delay differential equations with positive and negative coefficient. Applied Analysis. 27: 181-197.

Grammatikopoulos, M. K., Grove, E. A. & Ladas, G. 1986. Oscillations of first order neutral delay differential equations. J. Math. Anal. Appl. 120: 510-520.

Graef, J. R., Savithri R. & Thandapani, E. 2004. Oscillation of first order neutral delay differential equations, EJQTDE. No. 12: 1-12.

Graef, J. R., Grammatikopoulos, M. K. & Spikes, P. W. 1991. Asymptotic and oscillatory behaviour of solutions of first order nonlinear delay differential equations. J. Math. Anal. Appl. 155: 562-571.

Gyori I. & Ladas, G. 1991. Oscillation theory of delay differential equations. Oxford Mathematical Monographs. New York, Clarendon Press.

Hale, J. K. 1977. Theory of functional differential equations. New York, Springer.

Lalli, B. S. & Zhang, B. G. 1990. Oscillation of first order neutral differential equations. Appl. Anal. 39: 265-274.

Moaaz, O. and Al-Jaser, A. 2024. Functional differential equations of the neutral type: Oscillatory features of solutions. AIMS Mathematics, 9(6):16544-16563.

Ocalan, O. 2009. Existence of positive solutions for a neutral differential equation with positive and negative coefficients. Applied Mathematics Letters. 22: 84-90.

Onose, H. 1983. Oscillatory properties of the first order differential inequalities with deviating argument. Funkcialaj Ekvacioj. 26: 189-195.

Saker, S. H. & Kubiaczyk, I. 2002. Oscillation of solutions to nonlinear neutral delay differential equations. J. Appl. Anal. 8: 261-278.

Santra, Sh. S. 2016. Existence of positive solution and new oscilaation criteria for nonlinear first-order neutral delay differential equations. J. of Differential Equations & Applications. 8: 33-51.

Santra, Sh. S. & Scapellato, A. 2022. Some conditions for the oscillation of second-order differential equations with several mixed delays. J. of Fixed Point Theory and Applications. 24: 1-11.

Sficas, Y. G. & Stavroulakis, I. P. 1987. Necessary and sufficient conditions for oscillations of neutral differential equations. J. Math. Anal. Appl. 123:494-507.

Stavroulakis, I. P. 1989. Oscillation of mixed neutral equations. Hiroshima Math. J. 19: 441-456.

Yu, J. S., Chen, M. –P. & Zhang, H. 1998. Oscillation and nonoscillation in neutral equations with integrable coefficients. Computers Math. Applic. 35: 65-71.

Yu, J. S., Wang, Z. C. & Chuanxi, Q. 1992. Oscillation of neutral delay differential equations. Bull. Austral. Math. Soc. 45: 195-200.

Yu, Y. -H. 1991. Oscillation of solutions of neutral delay differential equations. Acta. Appl. Math. Sinica. 14: 404-410.

Zahariev, A. I. & Bainov, D. D. 1980. Oscillating properties of the solutions of a class of neutral type functional differential equations. Bull. Austral. Math. Soc. 22: 365-372.

Zhou, Y. 2000. Oscillation of neutral functional differential equations. Acta. Math. Hungar. 86: 205-212.