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Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions. (English) Zbl 1069.39002

The authors investigate a lot of conditions under which the first-order impulsive difference equation with periodic boundary condition

Δx(n)=f(n,x(n)),nn k ,n k {0,1,,N}:=J,Δx(n k )=I k (x(n k )),k=1,2,,p,x(0)=x(N),

where fC(J×,), I k C(,), 0<n 1 <n 2 <<n p <N, and N is a positive integer. Among others the method of upper and lower solution is used to prove the existence and uniqueness of so-called extremal solutions to the problem under consideration.

39A10Additive difference equations
39A12Discrete version of topics in analysis
34B15Nonlinear boundary value problems for ODE