New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations

Yuji Liu; Xingyuan Liu

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 4, page 337-360
  • ISSN: 0862-7959

Abstract

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This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is given to illustrate the main theorems obtained. One sees easily that Example 3.1 can not be solved by Theorems 2.1–2.3 obtained in Liu's paper since (G2) in Theorem 2.1, (G4) in Theorem 2.2 and (G6) in Theorem 2.3 are not satisfied.

How to cite

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Liu, Yuji, and Liu, Xingyuan. "New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations." Mathematica Bohemica 138.4 (2013): 337-360. <http://eudml.org/doc/260610>.

@article{Liu2013,
abstract = {This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is given to illustrate the main theorems obtained. One sees easily that Example 3.1 can not be solved by Theorems 2.1–2.3 obtained in Liu's paper since (G2) in Theorem 2.1, (G4) in Theorem 2.2 and (G6) in Theorem 2.3 are not satisfied.},
author = {Liu, Yuji, Liu, Xingyuan},
journal = {Mathematica Bohemica},
keywords = {anti-periodic solution; impulsive functional differential equation; fixed-point theorem; growth condition; anti-periodic solution; impulsive functional differential equation; fixed-point theorem; growth condition},
language = {eng},
number = {4},
pages = {337-360},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations},
url = {http://eudml.org/doc/260610},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Liu, Yuji
AU - Liu, Xingyuan
TI - New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 4
SP - 337
EP - 360
AB - This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is given to illustrate the main theorems obtained. One sees easily that Example 3.1 can not be solved by Theorems 2.1–2.3 obtained in Liu's paper since (G2) in Theorem 2.1, (G4) in Theorem 2.2 and (G6) in Theorem 2.3 are not satisfied.
LA - eng
KW - anti-periodic solution; impulsive functional differential equation; fixed-point theorem; growth condition; anti-periodic solution; impulsive functional differential equation; fixed-point theorem; growth condition
UR - http://eudml.org/doc/260610
ER -

References

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