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具有p-拉普拉斯算子的二阶非线性差分方程的无穷多个同宿解。

Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian.

作者信息

Sun Guowei, Mai Ali

机构信息

Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China.

Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China ; School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China.

出版信息

ScientificWorldJournal. 2014;2014:276372. doi: 10.1155/2014/276372. Epub 2014 May 14.

DOI:10.1155/2014/276372
PMID:24959604
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4052069/
Abstract

We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete p-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.

摘要

我们运用内哈里流形方法和临界点理论，研究具有强制权函数和超线性非线性的离散p-拉普拉斯方程非平凡同宿解的存在性。在不假设经典的安布罗塞蒂-拉宾诺维茨条件且无任何周期性假设的情况下，我们证明了该方程的存在性和多重性结果。