By employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p-Laplacian partial difference equation depending on a real parameter. To be specific, we give precise estimates of the parameter to guarantee that the considered problem possesses at least three solutions. Furthermore, based on a strong maximum principle, we show that two of the obtained solutions are positive under some suitable assumptions of the nonlinearity.

中文翻译：

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p- Laplacian偏离散Dirichlet边值问题的三个解

通过采用临界点理论，我们研究了依赖于实际参数的p-Laplacian偏差分方程的边值问题的解的存在性。具体来说，我们给出参数的精确估计值，以确保所考虑的问题至少具有三个解决方案。此外，基于强大的最大原理，我们证明了在某些适当的非线性假设下，所获得的两个解是正的。