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Periodic boundary value problem for first-order impulsive ordinary differential equations. (English) Zbl 1016.34023
The authors consider a periodic boundary value problem of the type $$x'(t)= f(t, x(t)),\quad t\ne t_k,\quad t\in J,\tag 1$$ $$\Delta x(t_k)= I_k(x(t_k)),\quad k= 1,2,\dots, p,\quad x(0)= x(T),$$ with $f\in C(J\times \bbfR,\bbfR)$, $J= [0,T]$, $I_k\in C(\bbfR,\bbfR)$, $\Delta x(t_k)= x(t^+_k)- x(t_k)$, $k= 1,2,\dots, p$, $0< t_1< t_2<\cdots< t_k<\cdots<\cdots< t_p< T$. By means of the method of upper and lower solutions and of the monotone iterative techniques, sufficient conditions for the existence of solutions to (1) are obtained.

34B37Boundary value problems for ODE with impulses
34A37Differential equations with impulses
Full Text: DOI
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