- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Regularity and multiplicity of solutions for a nonlocal problem with critical Sobolev-Hardy nonlinearities J. Korean Math. Soc.Published online February 10, 2020 Sarah Rsheed Mohamed Alotaibi and kamel saoudi University of Dammam, University of Sousse Abstract : In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, \begin{eqnarray*}({\rm P}) \left\{\begin{array}{ll} (-\Delta_p)^s u = \lambda |u|^{q-2}u + \frac{|u|^{p^*_s(t)-2}u}{|x|^t} \;\;\mbox{ in }\,\Omega ,\\ \\ u = 0 \;\;\mbox{ in }\,\mathbb{R}^N\setminus\Omega, \end{array} \right. \end{eqnarray*} %-\mu\frac{|u|^{p-2}u}{|x|^p} $0\leq \mu<\overline{\mu}:=\left(\frac{N-p}{p}\right)^p,$ where $\Omega\subset\R^N$ is a bounded domain with Lipschitz boundary, $00$ is a parameter, \$0