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Periodic boundary value problems of second-order impulsive differential equations. (English) Zbl 1176.34032

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)),
Δx(t k )=I k (x(t k )),Δx ' (t k )=I k * (x ' (t k )),
x(0)=x(T),x ' (0)=x ' (T)·

Here, k=1,2,,p, the functions I k , I k * are continuous, Δx(t k )=x(t k + )-x(t k ),

Δx ' (t k )=x ' (t k + )-x ' (t k ),

the right-hand side f satisfies the Carathéodory conditions. Monotone iterative technique is employed.

34B37Boundary value problems for ODE with impulses
34A45Theoretical approximation of solutions of ODE