Periodic solutions of impulsive systems with a small delay

For an impulsive system with delay it is proved that if the corresponding system without delay has an isolated omega -periodic solution, then in any neighbourhood of this orbit the system considered also has an omega -periodic solution if the delay is small enough.

[1]  Shui-Nee Chow,et al.  Existence of periodic solutions of autonomous functional differential equations , 1974 .

[2]  J. Hale Theory of Functional Differential Equations , 1977 .

[3]  J. Mallet-Paret Generic periodic solutions of functional differential equations , 1977 .

[4]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear autonomous functional differential equations , 1974 .

[5]  Periodic Solutions of Perturbed Neutral Differential Equations , 1974 .

[6]  C. Perelló Periodic solutions of differential equations with time lag containing a small parameter , 1968 .

[7]  A. Samoilenko,et al.  Periodic and almost-periodic solutions of impulsive differential equations , 1982 .

[8]  R. Grafton Periodic solutions of certain Lie´nard equations with delay , 1972 .

[9]  A. Iserles,et al.  Stability of the discretized pantograph differential equation , 1993 .

[10]  David Levin,et al.  Embedding of Delay Equations into an Infinite-Dimensional ODE System , 1995 .

[11]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear, autonomous functional differential equations. II , 1973 .

[12]  Arieh Iserles,et al.  On the generalized pantograph functional-differential equation , 1993, European Journal of Applied Mathematics.

[13]  H. Walther Existence of a non-constant periodic solution of a non-linear autonomous functional differential equation representing the growth of a single species population , 1975, Journal of mathematical biology.

[14]  James A. Yorke,et al.  Ordinary differential equations which yield periodic solutions of differential delay equations , 1974 .

[15]  Arieh Iserles,et al.  On nonlinear delay differential equations , 1994 .

[16]  Solutions périodiques des systèmes linéaires à argument retardé , 1967 .

[17]  Periodic solutions of differential equations with almost constant time lag , 1970 .

[18]  Juan J. Nieto,et al.  Periodic solutions of discontinuous impulsive differential systems , 1991 .

[19]  Arieh Iserles,et al.  Stability and Asymptotic Stability of Functional‐Differential Equations , 1995 .

[20]  Enrico Serra,et al.  Periodic solutions for some nonlinear differential equations of neutral type , 1991 .

[21]  G. S. Jones Periodic motions in banach space and applications to functional-differential equations. , 1962 .

[22]  J. Hale Solutions near simple periodic orbits of functional differential equations , 1970 .

[23]  Xinzhi Liu,et al.  Existence of periodic solutions of impulsive differential systems , 1991 .

[24]  Richard S. Hamilton,et al.  The inverse function theorem of Nash and Moser , 1982 .

[25]  G.Stephen Jones,et al.  The existence of periodic solutions of f′(x) = − αf(x − 1){1 + f(x)} , 1962 .

[26]  R. B. Grafton,et al.  A periodicity theorem for autonomous functional differential equations , 1969 .

[27]  Periodic solutions of a nonlinear autonomous age-dependent model of single species population dynamics , 1988 .

[28]  Yong Chen The existence of periodic solutions of the equation x′(t) = −ƒ(x(t), x(t − τ)) , 1992 .

[29]  Drumi D. Bainov,et al.  Impulsive Differential Equations with a Small Parameter , 1994, Series on Advances in Mathematics for Applied Sciences.

[30]  A note on Periodic of Nonlinear Differential Equations with Time Lag , 1967 .

[31]  A. Iserles,et al.  On the dynamics of a discretized neutral equation , 1992 .

[32]  J. Mawhin,et al.  On Periodic Solutions of Nonlinear Functional Differential Equations , 1999 .