论文标题
奇异的双向非局部椭圆形问题，与Choquard类型关键生长非线性
Singular doubly nonlocal elliptic problems with Choquard type critical growth nonlinearities
论文作者
论文摘要
涉及奇异非线性的椭圆方程理论是对椭圆形问题中奇异类型非线性与非本地非线性的相互作用进行了充分研究的。在本文中，我们研究了非常单数且双重的非本地单数问题$（P_λ）$（请参见下文）。首先，我们建立了非常弱的比较原则和最佳的Sobolev规律性。接下来，使用非平滑分析的临界点理论和能量功能的几何形状，我们建立了阳性弱解的全球多样性。
The theory of elliptic equations involving singular nonlinearities is well studied topic but the interaction of singular type nonlinearity with nonlocal nonlinearity in elliptic problems has not been investigated so far. In this article, we study the very singular and doubly nonlocal singular problem $(P_λ)$(See below). Firstly, we establish a very weak comparison principle and the optimal Sobolev regularity. Next using the critical point theory of non-smooth analysis and the geometry of the energy functional, we establish the global multiplicity of positive weak solutions.
