In this paper, we obtain a new sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems by using critical point theory in combination with periodic approximations. We prove that it is also necessary in some special cases. © 2010.
Zhou, Z., & Yu, J. (2010). On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems. Journal of Differential Equations, 249(5), 1199–1212. https://doi.org/10.1016/j.jde.2010.03.010