Copyright © 2012 Xiaofei He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
By establishing a new proper variational framework and using the critical point
theory, we establish some new existence criteria to guarantee that the 2th-order nonlinear difference equation containing both advance and retardation with -Laplacian , , , has infinitely many homoclinic orbits, where is -Laplacian operator; , , are nonperiodic in . Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.