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Existence of time periodic solutions for a class of non-resonant discrete wave equations

Zhang, Guang
; 
Feng, Wenying
; 
Yan, Yubin
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University of Chester
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2015-04-17
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Mathematics
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Abstract
In this paper, a class of discrete wave equations with Dirichlet boundary conditions are obtained by using the center-difference method. For any positive integers m and T, when the existence of time mT-periodic solutions is considered, a strongly indefinite discrete system needs to be established. By using a variant generalized weak linking theorem, a non-resonant superlinear (or superquadratic) result is obtained and the Ambrosetti-Rabinowitz condition is improved. Such a method cannot be used for the corresponding continuous wave equations or the continuous Hamiltonian systems; however, it is valid for some general discrete Hamiltonian systems.
Citation
Zhang, G., Feng, W., & Yan, Y. (2015). Existence of time periodic solutions for a class of non-resonant discrete wave equations. Advances in Difference Equations, 2015, 1. doi:10.1186/s13662-015-0457-z
Publisher
Springer
Journal
Advances in Difference Equations
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http://hdl.handle.net/10034/582661
DOI
10.1186/s13662-015-0457-z
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Article
Language
en
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The final publication is available at Springer via http://dx.doi.org/10.1186/s13662-015-0457-z
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ISSN
1687-1847
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http://www.advancesindifferenceequations.com/content/2015/1/120