Journal of the
Korean Mathematical Society JKMS

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, \[({\rm P}) \begin{cases} (-\Delta _p)^su = \lambda |u|^{q-2}u + \frac{|u|^{p^*_s(t)-2}u}{|x|^t} & \textrm{in} \ \Omega ,\\ u=0 & \textrm{in} \ \mathbb{R}^N\setminus\Omega, \end{cases} \] where $\Omega\subset\mathbb{R}^N$ is an open bounded domain with Lipschitz boundary, $00$ is a parameter, $0

Keywords: Nonlocal elliptic problems with Sobolev and Hardy nonlinearities, variational methods, multiple positive solutions, regularity of solutions

MSC numbers: Primary 34B15, 37C25, 35R20