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

Liu, Yuji ; Liu, Xingyuan

Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 337-360

Abstract (VO)

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.

Détail

DOI : 10.21136/MB.2013.143508

Classification : 34B16, 34C25
Keywords: anti-periodic solution; impulsive functional differential equation; fixed-point theorem; growth condition

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