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Zbl 1176.34032
Yao, Meiping; Zhao, Aimin; Yan, Jurang
Periodic boundary value problems of second-order impulsive differential equations. (English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 1, A, 262-273 (2009). ISSN 0362-546X

Sufficient conditions are obtained for the existence of solutions to periodic boundary value problem for second-order impulsive differential equations. The problems have the form $$x''(t)= f(t,x(t), x'(t)),$$ $$\Delta x(t_k)= I_k(x(t_k)),\ \Delta x'(t_k)= I^*_k(x'(t_k)),$$ $$x(0)= x(T),\quad x'(0)= x'(T).$$ Here, $k= 1,2,\dots, p$, the functions $I_k$, $I^*_k$ are continuous, $\Delta x(t_k)= x(t^+_k)- x(t_k)$, $$\Delta x'(t_k)= x'(t^+_k)- x'(t_k),$$ the right-hand side $f$ satisfies the Carathéodory conditions. Monotone iterative technique is employed.
[Sergei A. Brykalov (Ekaterinburg)]

MSC 2000:: *34B37 Boundary value problems with impulses
34A45 Theoretical approximation of solutions of ODE

Keywords: periodic solutions; impulsive differential equations; existence

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