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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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