Liouville type theorems, a priori estimates and existence of solutions for critical order Hardy-H\'{e}non equations in $\mathbb{R}^{n}$

• DOI: 10.48550/arxiv.1808.06609
• Publication Date: 2018-01-01
• Authors: Chen, Wenxiong; Dai, Wei; Qin, Guolin
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; 35B53 (Primary), 35B45, 35A01, 35J91 (Secondary); Analysis of PDEs (math.AP)

arXiv admin note: substantial text overlap with arXiv:1808.01581<br/>In this paper, we consider the critical order Hardy-H��non equations \begin{equation*} (-��)^{\frac{n}{2}}u(x)=\frac{u^{p}(x)}{|x|^{a}}, \,\,\,\,\,\,\,\,\,\,\, x \, \in \,\, \mathbb{R}^{n}, \end{equation*} where $n\geq4$ is even, $-\infty<br/>