By using critical point theory, we obtain a new sufficient condition on the existence of homoclinic solutions of a class of nonperiodic discrete nonlinear systems in infinite lattices. The classical Ambrosetti-Rabinowitz superlinear condition is improved by a general superlinear one. Some results in the literature are improved.
Genghong Lin. Zhan Zhou. "Homoclinic Solutions of a Class of Nonperiodic Discrete Nonlinear Systems in Infinite Higher Dimensional Lattices." Abstr. Appl. Anal. 2014 (SI18) 1 - 7, 2014. https://doi.org/10.1155/2014/436529