In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential. Using variational methods, we investigate the attainability of the corresponding minimization problem, and then obtain the existence of solutions. We also consider another Choquard type equation involving the p -Laplacian and critical nonlinearities in ℝN{\mathbb{R}^{N}}.

中文翻译：

---

具有双重临界非线性的Choquard型椭圆问题解的存在性。

在本文中，我们首先研究involvingN {\ mathbb {R} ^ {N}}中涉及局部拉普拉斯算子和Hardy–Sobolev–Maz'ya势的非局部椭圆问题的非平凡解的存在。使用变分方法，我们研究了相应的最小化问题的可及性，然后获得了解的存在性。我们还考虑了另一个涉及-N {\ mathbb {R} ^ {N}}中的p -Laplacian和临界非线性的Choquard型方程。