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Zbl 1067.39022
Yu, Jianshe; Long, Yuhua; Guo, Zhiming
Subharmonic solutions with prescribed minimal period of a discrete forced pendulum equation. (English)
[J] J. Dyn. Differ. Equations 16, No. 2, 575-586 (2004). ISSN 1040-7294; ISSN 1572-9222/e

Using variational methods the authors obtain sufficient conditions on the existence of sub-harmonic solutions with prescribed minimal period $pT$ for the second order difference equation $$x(n+1)-2x(n)+x(n-1)+A \sin(x(n))=f(n),\quad f(n+T)=f(n).$$ An example is given. The idea of the paper is to find variational functionals to transfer the existence of sub-harmonic solutions into the existence of critical points of the corresponding functional. \par This reviewer likes to add that the matrix $B$ on page 579 in the paper is a circulant matrix some of its properties are well known [{\it S. Barnett}, Matrices: Methods and applications, Oxford University Press (1990; Zbl 0706.15001)].
[Ahmed Hegazi (Mansoura)]

MSC 2000:: *39A11 Stability of difference equations
39A12 Discrete version of topics in analysis
70J35 Forced motions

Keywords: second order difference equation; periodic solution; subharmonic solution; critical point; minimal period; discrete forced pendulum equation

Citations: Zbl 0706.15001

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