In the paper, we study the existence of weak solutions for a class of new nonlocal problems involving a -Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, we prove that the new -Kirchhoff problem has at least two nontrivial weak solutions.

中文翻译：

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一个新的-基尔霍夫型椭圆问题的非平凡解的多样性

在本文中，我们研究了一类新的非局部问题涉及 a - Laplacian 算子的弱解的存在性。通过使用埃克兰变分原理和山口定理，我们证明了新-基尔霍夫问题至少有两个非平凡弱解。