Periodic solutions of higher-order delay differential equations

Liu, Yuji; Yang, Pinghua; Ge, Weigao

doi:10.1016/j.na.2005.04.038

Cited by 14 publications

(11 citation statements)

References 21 publications

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“…(1.1). Our method is different from [18], and the results are related to not only b i and the x 0 , x 1 , . .…”

Section: X(t) X T − τ (T) X (T) + E(t)mentioning

confidence: 99%

“…In recent years, there are many papers studying the existence of periodic solutions of the first or higher order differential equations [1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For example, in [11], Lu and Ge studied the following differential equations with a deviating argument:…”

Section: M) With P(t + T ) = P(t) τ I (T + T ) = τ I (T)mentioning

confidence: 99%

“…In [4][5][6][7][8][9]14,16,18], n, 2n and 2n + 1 order differential equations were discussed, the types of the equations as follows: In [18], Liu studied the existence of periodic solutions of the following differential equations:…”

Section: X(t) X T − τ (T) X (T) + E(t)mentioning

confidence: 99%

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Periodic solutions for higher order differential equations with deviating argument

Pan¹

2008

Journal of Mathematical Analysis and Applications

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“…(1.1). Our method is different from [18], and the results are related to not only b i and the x 0 , x 1 , . .…”

Section: X(t) X T − τ (T) X (T) + E(t)mentioning

confidence: 99%

Section: M) With P(t + T ) = P(t) τ I (T + T ) = τ I (T)mentioning

confidence: 99%

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Periodic solutions for higher order differential equations with deviating argument

Pan¹

2008

Journal of Mathematical Analysis and Applications

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“…There have been many papers concerned with the existence of periodic solutions of the differential equations without delays

x^{(n)} (t) MathClass-rel= f ((), t MathClass-punc, x (t) MathClass-punc, x MathClass-rel' (t) MathClass-punc, MathClass-rel\dots MathClass-punc, x (n MathClass-bin- 1) (t)) MathClass-punc, t MathClass-rel\in R MathClass-punc,

or with delays

x^{(n)} (t) MathClass-rel= f (t MathClass-punc, x (t) MathClass-punc, x (t MathClass-bin- τ_{1} (t)) MathClass-punc, MathClass-rel\dots MathClass-punc, x (t MathClass-bin- τ_{m} (t))) MathClass-punc, t MathClass-rel\in R MathClass-punc,

one may see and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The existence of periodic solutions of higher order nonlinear periodic difference equations

Liu

2012

Math Methods in App Sciences

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Sufficient conditions for the existence of at least one periodic solution of two classes of nonlinear higher order periodic difference equations are established, respectively. The results show us that sufficient conditions for the existence of T − periodic solutions of difference equation are different from those ones for the existence of T − periodic solutions of differential equation. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Recently, various problems associated to a MFDE (as, for example, the existence of analytic solutions for an equation with analytic data) were studied by Dârzu in [5,6], Rus and Dârzu-Ilea in [14] and Precup in [13]. The authors of [7,[9][10][11] studied the existence of periodic solutions for some MFDE. They use the coincidence degree theory as developed by Gaines and Mawhin in [8].…”

Section: Introductionmentioning

confidence: 99%