On the solvability of anti-periodic boundary value problems with impulses. (English) Zbl 1186.34037
Summary: We are concerned with the existence of solutions for the second order impulsive anti-periodic boundary value problem
\[ \begin{cases} u''(t) + f(t,u(t),u'(t))=0, \quad & t \not= t_k, \;t \in [0, T], \\ \triangle u(t_k) = I_k(u(t_k)), & k = 1, \cdots , m, \\ \triangle u'(t_k) = I_k^*(u(t_k)), & k = 1, \cdots , m, \\ u(0) + u(T) = 0, \;u'(0) + u'(T) = 0. \end{cases} \]
New existence criteria are established based on Schaefer’s fixed-point theorem.
\[ \begin{cases} u''(t) + f(t,u(t),u'(t))=0, \quad & t \not= t_k, \;t \in [0, T], \\ \triangle u(t_k) = I_k(u(t_k)), & k = 1, \cdots , m, \\ \triangle u'(t_k) = I_k^*(u(t_k)), & k = 1, \cdots , m, \\ u(0) + u(T) = 0, \;u'(0) + u'(T) = 0. \end{cases} \]
New existence criteria are established based on Schaefer’s fixed-point theorem.
MSC:
34B37 | Boundary value problems with impulses for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |