The aim of this paper is to prove the existence of two solutions for a nonlinear elliptic problem involving the $(p,q)$‐Laplacian operator. The solutions are obtained by using variational methods and critical points theorems. The positivity of the solutions is shown by applying a generalized version of the strong maximum principle.

中文翻译：

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（p，q）-Laplacian Dirichlet问题的两个正解

本文的目的是证明涉及非线性椭圆问题的两个解的存在性。 $（p，q）$‐拉普拉斯算子。通过使用变分方法和临界点定理获得解。通过应用强最大原理的广义形式可以显示解决方案的积极性。