Periodic boundary value problems for second order impulsive differential systems. (English) Zbl 0712.34033

Hu, Shouchuan; Lakshmikantham, V.

Nonlinear Anal., Theory Methods Appl. 13, No. 1, 75-85 (1989).

The authors study the question on solvability of the boundary value problem \[ x''=f(t,x,x'),\quad x(t_ k+)=I_ k(x(t_ k-)),\quad x'(t_ k+)=N_ k(x'(t_ k-))\quad (k=1,...,p),\quad x(0)=x(T),\quad x'(0)=x'(T) \] where the function f: [0,T] \(\times R^{2n}\to R^ n\) is continuous on \((]0,T[\setminus \{t_ 1,...,t_ p\})\times R^{2n}\), \(t_ k\in]0,T[\) and the components of the vector functions \(I_ k\), \(N_ k: R^ n\to R^ n\) \((k=1,...,p)\) are nondecreasing in each variable.

Reviewer: B.Shekhter

MSC:

34B15

Nonlinear boundary value problems for ordinary differential equations

Keywords:

second order differential equation; solvability

References:

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