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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.

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