ON THE BEHAVIORS OF SOLUTIONS IN LINEAR NONHOMOGENEOUS DELAY DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

Abstract

This paper deals with the behaviors of solutions for linear nonhomogeneous delay differential equations. In this study, a periodic solution, an asymptotic result and a useful exponential estimate of the solutions are established. Our results are obtained by the use of real roots of the corresponding characteristic equation.

Keywords

• DELAY DIFFERENTIAL EQUATION
• PERIODIC COEFFICIENT
• NONHOMOGENEOUS
• SOLUTIONS

References

1. A. Ashyralyev, H. Akca, Stability estimates of difference schemes for neutral delay dfferential equations, Nonlinear Analysis, 44 (2001) 443-452.
2. R. Bellman, K. Cooke, Differential-Difference Equations, Academic Press: New York, NY, USA, 1963.
3. R.D. Driver, Ordinary and Delay Differential Equations, Springer: New York, NY, USA, 1977.
4. M.V.S. Frasson, S.M.V. Lunel, Large Time Behaviour of Linear Functional Differential Equations, Integral Equations and Operator Theory, 47 (2003) 91–121.
5. V. Kolmanovski, A. Myshkis, Applied Theory of Functional Differential Equations, Kluver Academic: Dordrecht, The Netherlands, 1992.
6. A.F. Yeniçerioğlu, V. Yazıcı, C. Yazıcı, Asymptotic Behavior and Stability in Linear Impulsive Delay Differential Equations with Periodic Coefficients, Mathematics, 8 (2020) 1802.
7. N.E. Kobrinskii, V.I. Kus'min, Accuracy of Economic-Mathematical models, Finansy and Statistica, Moscow, 1981.
8. M. Farkas, Periodic Motions, Applied Mathematical Sciences 104, Springer-Verlag, New York, Inc., 1994.

9. Ch.G. Philos, Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations, Proceedings of the Royal Society of Edinburgh, 128A, 128 (1998) 1371-1387.
10. Ch.G. Philos, and I.K. Purnaras, Periodic first order linear neutral delay differential equations, Applied Mathematics and Computation, 117 (2001) 203-222.
11. M. Farkas, Asymptotic Periodicity of Delay Differential Equations, Journal of Mathematical Analysis and Applications, 226 (1998) 150-165.