Existence and uniqueness results for discrete second-order periodic boundary value problems. (English) Zbl 1057.39008

Atici, F. M.; Cabada, A.

Comput. Math. Appl. 45, No. 6-9, 1417-1427 (2003).

The paper contains results on existence and uniqueness of a second order nonlinear difference equation \[ - \Delta^2 y(n-1) + q(n) y(n) = f(n,y(n)), \] \(\Delta\) the forward difference operator, with periodic boundary conditions. The methods used in the proofs are based on the notions of lower and upper solutions, Green’s functions and Brouwer’s fixed point theorem.

Reviewer: Stefan Hilger (Eichstätt)

MSC:

39A12	Discrete version of topics in analysis
34B15	Nonlinear boundary value problems for ordinary differential equations
39A11	Stability of difference equations (MSC2000)

Keywords:

second order nonlinear difference equation; periodic boundary conditions; upper and lower solutions; Green’s functions; periodic solution

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