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Luo, Zhiguo; Shen, Jianhua; Nieto, J. J.

Antiperiodic boundary value problem for first-order impulsive ordinary differential equations. (English) Zbl 1084.34018

Comput. Math. Appl. 49, No. 2-3, 253-261 (2005).
The authors consider the antiperiodic boundary value problem for an impulse differential equation of the form \[ \begin{gathered} x'(t)+\lambda x(t)= F(t,x(t)),\quad t\in J,\;t\neq t_k,\\ \Delta x(t_k)= I_k(x(t_k)),\quad k= 1,2,\dots, m,\\ x(0)= -x(T),\end{gathered} \] with \(t\in J= [0,T]\), \(t\neq t_k\), \(\lambda> 0\).
Sufficiently conditions for the existence of a solution are derived.
Reviewer: Stepan Kostadinov (Plovdiv)

Cited in 45 Documents

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34A37 Ordinary differential equations with impulses

Keywords:

impulse differential equations; antiperiodic boundary value problem; Leray-Schauder alternative; monotone iterative technique
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References:

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