Zhang, GuangFeng, WenyingYan, Yubin2015-11-252015-11-252015-04-17Zhang, 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-z1687-184710.1186/s13662-015-0457-zhttp://hdl.handle.net/10034/582661The final publication is available at Springer via http://dx.doi.org/10.1186/s13662-015-0457-zIn 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.enArchived with thanks to Advances in Difference EquationsWave equationHamiltonian systemAmbrosetti-Rabinowitz conditionstrongly indefinite discrete systemtime mT-periodic solutionvariant generalized weak linking theoremArticleAdvances in Difference Equations