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Zbl 1073.39009
Yu, Jianshe; Guo, Zhiming; Zou, Xingfu
Periodic solutions of second order self-adjoint difference equations.
(English)
[J] J. Lond. Math. Soc., II. Ser. 71, No. 1, 146-160 (2005). ISSN 0024-6107; ISSN 1469-7750/e

The paper is concerned with periodic solutions of second order self-adjoint difference equations of the form $$\Delta\lbrack p(t)\Delta u(t-1)]+q(t)u(t)=f(t,u(t)),\tag{*}$$ where $\Delta$ is the forward difference operator; $p:{\Bbb Z}\to {\Bbb R}$ with $p(t)\neq 0$ for each $t\in {\Bbb Z}$, $q: {\Bbb Z}\to {\Bbb R}$ and $f: {\Bbb Z}\times {\Bbb R}\to {\Bbb R}$ 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 ($*$).
[Nguyen Van Minh (Carrollton)]
MSC 2000:
*39A11 Stability of difference equations
39A12 Discrete version of topics in analysis

Keywords: periodic solution; second order difference equation; critical point theory

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