Abstract
In this paper, by using the Krasnoselskii fixed point theorem on cone compression and expansion, we study the existence of positive periodic solutions of differential equations with impulses and delays, and obtain some new results.
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V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
D.D. Bainov and P.S. Simeonov, Systems with Impulse Effect: Stability Theory and Applications, Horwood, Chicester, 1989.
Jiang Daqing, Wei Zunji, Existence of periodic positive solutions of non-autonomous functional differential equations, Chin. Math. Ann., 20A, 6(1999), 715–720, [in chinese].
J.H. Shen and J. Yan, Razumikhin type stability theorems for impulsive functional differential equations, Nonlinear Anal, 33(1998), 519–531.
Z. Luo and J. Shen, Stability results for impulsive functional differential equations with infinite delays, J. Comput. Applied Math., 131(2001), 55–64.
Li Yong and Zhou Qin-De, Periodic solutions to ordinary differential equations with impulses, Science in China., Series A, 36, 7 (1993), 778–790.
F. Merdiverci Alici and G.Sh. Guseinov, Positive periodic solutions for nonlinear difference equations with periodic coefficients, J. Math. Anal. Appl., 232 (1999), 166–182.
Wang H., On the existence of positive solutions for semilinear elliptic equations in the Annulus, J. Diff. Eqns., 109(1994), 1–8.
Chow, S. N., Existence of periodic solutions of autonomous functional differential equations, J. Diff. Eqns., 15(1974), 350–375.
Drumi Bainov and Pavel Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, 1993.
M. Bachar and P. Magal, Existence of periodic solutions for a class of delay differential equations with impulses, Fields Institute communications, 29(2001), 37–49.
G. Ballinger and X. Liu, On boundedness of solutions of impulsive systems, Nonlinear Studies, 4, No.1 (1997), 121–1
G. Ballinger and X. Liu, Existence and uniqueness results for impulsive delay differential equations, DCDIS, 5(1999), 579–591.
J.K. Hale and S.M.V. Lunel, Introduction to Functional Differential Equations, Springer-Velag, New York, 1993.
G. Ballinger and X. Liu, Permanence of population growth models with impulsive effects, Math. and Computer Modelling, 26(1997), 59–72.
G. Ballinger and X. Liu, Existence, uniqueness and boundedness results for impulsive delay differential equations, Appl. Anal., 74(2000), 71–93.
J. Yan and J. Shen, Impulsive stabilization of functional differential equation by Liapunov-Razumikhin functions, Nonlinear Anal., 37(1999), 245–255.
X. Liu, Stability results for impulsive differential systems with applications to population growth models, Dynamics and Stability of Systems, 9(1994), 163–174.
X. Liu and J.H. Shen, Razumikhin-type theorems on boundedness for impulsive functions differential equations, Dynamic Systems Appl., 9(2000), 389–404.
X. Liu and G. Ballinger, Uniform asymptotic stability of impulsive differential equations, Comuters Math. Appl., 41(2001), 903–915.
Deimling K., Nonlinear Functional Analysis, Springer Verlag, Berlin, 1985.
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This work is supported by the NNSF of China (No. 10071018) and the EYTP of China.
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Li, J., Shen, J. On Positive Periodic Solutions to Impulsive Differential Equations with Delays. Results. Math. 45, 67–78 (2004). https://doi.org/10.1007/BF03322998
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DOI: https://doi.org/10.1007/BF03322998