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Periodic solutions of second order self-adjoint difference equations. (English) Zbl 1073.39009
The paper is concerned with periodic solutions of second order self-adjoint difference equations of the form \[ \Delta[ p(t)\Delta u(t-1)]+q(t)u(t)=f(t,u(t)),\tag{\(*\)} \] where \(\Delta\) is the forward difference operator; \(p:{\mathbb Z}\to {\mathbb R}\) with \(p(t)\neq 0\) for each \(t\in {\mathbb Z}\), \(q: {\mathbb Z}\to {\mathbb R}\) and \(f: {\mathbb Z}\times {\mathbb R}\to {\mathbb R}\) are \(T\)-periodic in \(t\), and \(f\) is continuous in the second variable. Using the critical point theory, the authors give several sufficient conditions for the existence of \(T\)-periodic solutions of (\(*\)).

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
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