On the solvability of anti-periodic boundary value problems with impulses

Chuanzhi Bai, Huaiyin Teachers College, Huaian, Jiangsu, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 11. (2009), pp. 1-15.

Abstract: In this paper, we are concerned with the existence of solutions for second order impulsive anti-periodic boundary value problem
${ \left \{\begin{array} {l}
u''(t) + f(t,u(t),u'(t))=0, \quad t \not= t_k, \ t \in [0, T], \\
\triangle u(t_k) = I_k(u(t_k)), \quad k = 1, \cdots , m, \\
\triangle u'(t_k) = I_k^*(u(t_k)), \quad k = 1, \cdots , m, \\
u(0) + u(T) = 0, \ u'(0) + u'(T) = 0.
\end{array}\right.} $
New criteria are established based on Schaefer's fixed-point theorem.

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