Homoclinic solutions in non-periodic discrete ϕϕ-Laplacian equations with mixed nonlinearities

By using critical point theory, we obtain some sufficient conditions on the existence of homoclinic solutions of a class of non-periodic discrete ϕϕ-Laplacian equations. In our paper, the nonlinearities can be mixed super pp-linear with asymptotically pp-linear at ∞∞ for p≥1p≥1, and be mixed superlinear with asymptotically linear at 00. To the best of our knowledge, there is no such result for the existence of homoclinic solutions in non-periodic discrete ϕϕ-Laplacian equations before. Some results in the literature are improved.