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Asymptotic behaviour of solutions to linear neutral delay differential equations with periodic coefficients
1. | Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo -- Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil, Brazil |
References:
[1] |
R. D. Driver, Some harmless delays, Delay and functional differential equations and their applications (Proc. Conf., Park City, Utah, 1972), New York: Academic Press, (1972), 103-119. |
[2] |
R. D. Driver, D. W. Sasser and M. L. Slater, The equation $x' (t)=ax(t)+bx(t-\tau )$ with "small'' delay, Amer. Math. Monthly, 80 (1973), 990-995.
doi: 10.2307/2318773. |
[3] |
M. V. S. Frasson, On the dominance of roots of characteristic equations for neutral functional differential equations, Appl. Math. Comput., 214 (2009), no. 1, 66-72.
doi: 10.1016/j.amc.2009.03.058. |
[4] |
M. V. S. Frasson and S. M. Verduyn Lunel, Large time behaviour of linear functional differential equations, Integral Equations Operator Theory, 47 (2003), 91-121.
doi: 10.1007/s00020-003-1155-x. |
[5] |
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, Applied Mathematical Sciences, 99 New York: Springer-Verlag, 1993. |
[6] |
V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional-Differential Equations, vol. 463 of Mathematics and its Applications, Dordrecht: Kluwer Academic Publishers, 1999. |
[7] |
I.-G. E. Kordonis, N. T. Niyianni and C. G. Philos, On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations, Arch. Math. (Basel), 71 (1998), 454-464.
doi: 10.1007/s000130050290. |
[8] |
J. C. Lillo, Periodic differential difference equations, J. Math. Anal. Appl., 15 (1966), 434-441. |
[9] |
C. G. Philos, Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), 1371-1387.
doi: 10.1017/S0308210500027372. |
[10] |
C. G. Philos and I. K. Purnaras, Periodic first order linear neutral delay differential equations, Appl. Math. Comput., 117 (2001), 203-222.
doi: 10.1016/S0096-3003(99)00174-5. |
show all references
References:
[1] |
R. D. Driver, Some harmless delays, Delay and functional differential equations and their applications (Proc. Conf., Park City, Utah, 1972), New York: Academic Press, (1972), 103-119. |
[2] |
R. D. Driver, D. W. Sasser and M. L. Slater, The equation $x' (t)=ax(t)+bx(t-\tau )$ with "small'' delay, Amer. Math. Monthly, 80 (1973), 990-995.
doi: 10.2307/2318773. |
[3] |
M. V. S. Frasson, On the dominance of roots of characteristic equations for neutral functional differential equations, Appl. Math. Comput., 214 (2009), no. 1, 66-72.
doi: 10.1016/j.amc.2009.03.058. |
[4] |
M. V. S. Frasson and S. M. Verduyn Lunel, Large time behaviour of linear functional differential equations, Integral Equations Operator Theory, 47 (2003), 91-121.
doi: 10.1007/s00020-003-1155-x. |
[5] |
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, Applied Mathematical Sciences, 99 New York: Springer-Verlag, 1993. |
[6] |
V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional-Differential Equations, vol. 463 of Mathematics and its Applications, Dordrecht: Kluwer Academic Publishers, 1999. |
[7] |
I.-G. E. Kordonis, N. T. Niyianni and C. G. Philos, On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations, Arch. Math. (Basel), 71 (1998), 454-464.
doi: 10.1007/s000130050290. |
[8] |
J. C. Lillo, Periodic differential difference equations, J. Math. Anal. Appl., 15 (1966), 434-441. |
[9] |
C. G. Philos, Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), 1371-1387.
doi: 10.1017/S0308210500027372. |
[10] |
C. G. Philos and I. K. Purnaras, Periodic first order linear neutral delay differential equations, Appl. Math. Comput., 117 (2001), 203-222.
doi: 10.1016/S0096-3003(99)00174-5. |
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