Title: Multiplicity of solutions for singular elliptic problems with Stein-Weiss term Show Chinese title

Title: 具有Stein-Weiss项的奇异椭圆问题的解的多重性

Abstract: In the present work, we establish the existence and multiplicity of positive solutions for the singular elliptic equations with a double weighted nonlocal interaction term defined in the whole space $\mathbb{R}^N$. The nonlocal term and the fact that the energy functional is not differentiable are the main difficulties for this kind of problem. We apply the Nehari method and the nonlinear Rayleigh quotient to prove that our main problem has at least two positive weak solutions. Furthermore, we prove a nonexistence result related to the extreme $\lambda^*> 0$ given by the nonlinear Rayleigh quotient. Show Chinese abstract

Abstract: 在本文中，我们建立了在全空间$\mathbb{R}^N$中定义的具有双加权非局部相互作用项的奇异椭圆方程正解的存在性和多重性。 非局部项以及能量泛函不可微的事实是此类问题的主要困难。 我们应用Nehari方法和非线性Rayleigh商来证明我们的主要问题至少有两个正弱解。 此外，我们证明了一个与非线性Rayleigh商给出的极端$\lambda^*> 0$相关的不存在性结果。