Fractional elliptic equations with Hardy potential and critical nonlinearities

Abstract

In this paper, we consider the fractional elliptic equation \begin{align*} \left\{\begin{aligned} &(-Δ)^s u-μ\frac{u}{|x|^{2s}} = \frac{|u|^{2_s^\ast (α)-2}u}{|x|^α} + f(x,u), && \mbox{in} \ Ω,\\ &u=0, && \mbox{in} \ \mathbb{R}^{n}\backslash \ Ω, \end{aligned}\right. \end{align*} where $\Omega \subset R^n$ is a smooth bounded domain, $0\in \Omega$, $0<s<1$, $0<\alpha <2s<n$, $2_s^{\ast }(\alpha )=\frac{2(n-\alpha )}{n-2s}$. Under some assumptions on $\mu$ and $f$, we obtain the existence of nonnegative solutions.

References in corpus (1)

• Existence Result for Non-linearly Perturbed Hardy-Schrödinger Problems: Local and Non-local cases