Abstract

In this article, we are concerned with the existence of at least one, two and three distinct solutions for discrete boundary value problems driven by the Laplacian. The proof of the main result depends on variational methods. By using a consequence of the local minimum theorem due Bonanno we investigate the existence of at least one solution and two solutions for the problem with the weight. Furthermore, by using two critical point theorems, one due Averna and Bonanno, and another due Bonanno we explore the existence of two and three solutions for the problem. We also provide two examples in order to illustrate the main results.

摘要

在本文中，我们关注由拉普拉斯算子驱动的离散边值问题是否存在至少一个、两个和三个不同的解。主要结果的证明依赖于变分方法。通过使用 Bonanno 的局部最小定理的结果，我们研究了权重问题的至少一个解和两个解的存在性。此外，通过使用两个临界点定理，一个是 Averna 和 Bonanno 提出的，另一个是 Bonanno 提出的，我们探索了问题的两个和三个解的存在性。我们还提供了两个例子来说明主要结果。