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Boundary value problem of second order impulsive functional differential equations. (English) Zbl 1111.34047

The authors use the so-called method of upper and lower solutions to provide existence results to a boundary value problem for second-order impulsive functional-differential equations.
Although they state in the introduction the impulsive condition \[ x(t_k^+)-x(t_k^-)=I_k(x(t_k)),\quad k=1,\dots, p, \] it turns out that in all existence results it is assumed that \(I_k(x(t_k))=L_kx'(t_k)\) with \(L_k\geq 0\). Thus, the results obtained are only valid for a very particular family of differential equations with impulses.
Reviewer: Eduardo Liz (Vigo)

MSC:

34K10 Boundary value problems for functional-differential equations
34K45 Functional-differential equations with impulses
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