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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 $$\gather \Delta x(n)= f(n,x(n)),\quad n\ne n_k,\quad n_k\in \{0,1,\dots, N\}:= J,\\ \Delta x(n_k)= I_k(x(n_k)),\quad k= 1,2,\dots, p,\\ x(0)= x(N),\endgather$$ where $f\in C(J\times\bbfR,\bbfR)$, $I_k\in C(\bbfR,\bbfR)$, $0< n_1< n_2<\cdots< n_p< N$, 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
Full Text: DOI
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