This paper derives several sufficient conditions for the existence of three solutions to the Dirichlet problem for a second-order self-adjoint difference equation involving p-Laplacian through the critical point theory. Furthermore, by using the strong maximum principle, we prove that the three solutions are positive under appropriate assumptions on the nonlinearity. Finally, we present three examples to confirm our results.

中文翻译：

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涉及p -Laplacian的二阶自伴随差分方程Dirichlet问题的三种解决方案

本文通过临界点理论，为涉及p -Laplacian的二阶自伴随差分方程的Dirichlet问题的三个解的存在导出了几个充分的条件。此外，通过使用强最大原理，我们证明了在适当的非线性假设下这三个解是正的。最后，我们给出三个例子来证实我们的结果。