We are interested in the existence and multiplicity of ground state solutions for a class of p(x)-Laplacian Dirichlet problem in bounded domains. Firstly, combining constraint variational method and quantitative deformation lemma, we prove that the equation possesses at least one least energy sign-changing solution with exactly two nodal domains. Finally, using a strong maximum principle, we obtain three ground state solutions (one positive, one negative, and one sign-changing) for this problem.

中文翻译：

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一类涉及 p(x)-Laplacian 的椭圆 Dirichlet 问题的基态解

我们对有界域中一类p ( x )-Laplacian Dirichlet 问题的基态解的存在性和多样性感兴趣。首先，结合约束变分法和定量变形引理，证明该方程至少具有一个具有两个节点域的最小能量符号变化解。最后，使用强最大值原理，我们获得了此问题的三个基态解（一个正、一个负和一个符号改变）。