一階時滯微分方程正周期解的存在性

張 露, 劉瑞寬

(西北師范大學數學與統計學院,甘肅蘭州730070)

1 主要結果

2 預備知識

3 主要結果的證明

[1]Gurney W S,Nisbet S P.Nicholson's blowles revisited[J].Nature,1980,287:17-21.

[2]Mackey M C,Glass L.Oscillations and chaos in physiological control systems[J].Science,1997,197:287-289.

[3]Freedman H I,Wu J.Positive solutions of single-species modles with periodic delay[J].J Math Anal Appl,1992,23:689-701.

[4]Jiang D,Wei J.Existence of positive periodic solutions of non-autonomous functinal differential equations[J].Chinese Ann Math,1999,A20(6):715-720.

[5]Jiang D,Wei J,Zhang B.Positive periodic solutions of functinal differential equations and population modles[J].J Differential Integral,2002,71:1-13.

[6]Chen L,Sun J.Nonlinear boundary value problem for first order impulsive functional differential equations[J].J Math Anal Appl,2006,318:726-741.

[7]Wazewska-Czyzewska M,Lasota A.Mathematical problems of the dynamics of a system of red blood cells[J].Mat Stosow,1976,6:23-40.

[8]Wu J,Wang Z.Positive periodic solution of second-order nonlinear differrntialsystems with two parameters[J].Comput Math Appl,2008,56:43-54.

[9]Wang A,Jiang D.Existence of positive periodic solutions for functional differential equations[J].Kyushu Math,2002,56:193-202.

[10]楊丹丹,李剛.一階非線性脈沖微分方程邊值問題解的存在性[J].四川師范大學學報:自然科學版,2010,33(6):763-767.

[11]Cheng S,Zhang G.Existence of positive periodic solutions for non-autonomous functional differential equations[J].Electron J Differential Equations,2001,59:1-8.

[12]Jin Z,Wang H.A note on periodic solutions of functional differential equations[J].Appl Math Lett,2010,23:581-584.

[13]Deimling K.Nonlinear Functional Analysis[M].Berlin:Springer-Verlag,1985.

[14]Guo D,Lakshmikantham V.Nonlinear Problems in Abstract Cones[M].Orlando:Academic Press,1988.

[15]Krasnoselskii M.Positive Solutions of Operator Equations[M].Groningen:Noordhoff,1964.

[16]Wang H.Positive periodic solutions of functional differential systems[J].J Diff Equations,2004,202:354-366.