In this paper, we study the multiplicity of weak solutions to the boundary value problem where Ω is a bounded domain with smooth boundary in is odd in ξ and is a perturbation term. Under some growth conditions on f and g, we show that there are infinitely many weak solutions to the problem. Here we do not require that f satisfies the Ambrosetti-Rabinowitz (AR) condition. The conditions on f and g are relatively weak and our result is new even in the case , i.e. for the classical Laplace equation with the Dirichlet boundary condition.

中文翻译：

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一类涉及 Grushin 算子的扰动退化椭圆方程的无穷多解

在本文中，我们研究了边值问题的多重弱解，其中 Ω 是一个有界域，平滑边界 in 在 ξ 中是奇数，并且是一个扰动项。在 f 和 g 的某些增长条件下，我们表明该问题有无限多个弱解。这里我们不要求 f 满足 Ambrosetti-Rabinowitz (AR) 条件。f 和 g 上的条件相对较弱，即使在 情况下我们的结果也是新的，即对于具有 Dirichlet 边界条件的经典拉普拉斯方程。