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Zbl 1057.39008
Atici, F.M.; Cabada, A.
Existence and uniqueness results for discrete second-order periodic boundary value problems. (English)
[J] Comput. Math. Appl. 45, No. 6-9, 1417-1427 (2003). ISSN 0898-1221

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.
[Stefan Hilger (Eichstätt)]

MSC 2000:: *39A12 Discrete version of topics in analysis
34B15 Nonlinear boundary value problems of ODE
39A11 Stability of difference equations

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

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