Solutions for a nonlocal elliptic equation involving critical growth and Hardy potential

Abstract

In this paper, by an approximating argument, we obtain infinitely many solutions for the following Hardy-Sobolev fractional equation with critical growth \begin{equation*}\label{0.1} \left\{% \begin{array}{ll} (-Δ)^{s} u-\ds\frac{μu}{|x|^{2s}}=|u|^{2^*_s-2}u+au, & \hbox{$\text{in}\Omega$},\vspace{0.1cm} u=0,\,\, &\hbox{$\text{on}\partial \Omega$}, \\ \end{array}% \right. \end{equation*} provided $N>6s$, $\mu \ge 0$, $0<s<1$, $2_s^{\ast }=\frac{2N}{N-2s}$, $a>0$ is a constant and $\Omega$ is an open bounded domain in ${\mathbb{R}}^N$ which contains the origin.

References in corpus (3)

• Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow
• Non degeneracy of the bubble in the critical case for non local equations
• Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings