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

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• 作者：Genghong Lin ; Zhan Zhou ; ^{zzhou0321@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Homoclinic solution ; Discrete ϕϕ-Laplacian ; Mixed nonlinearity ; Critical point theory ; Non-periodic
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：64
• 期：Complete
• 页码：15-20
• 全文大小：575 K

文摘

By using critical point theory, we obtain some sufficient conditions on the existence of homoclinic solutions of a class of non-periodic discrete ϕ$\varphi$-Laplacian equations. In our paper, the nonlinearities can be mixed super p$p$-linear with asymptotically p$p$-linear at ∞$\infty$ for p≥1$p\ge 1$, and be mixed superlinear with asymptotically linear at 0$0$. To the best of our knowledge, there is no such result for the existence of homoclinic solutions in non-periodic discrete ϕ$\varphi$-Laplacian equations before. Some results in the literature are improved.