Abstract
In this paper, we have used variational methods to study existence of solutions for the following critical nonlocal fractional Hardy elliptic equation \begin{equation*} (- \Delta)^s u - \gamma \frac{u}{|x|^{2 s}} = \frac{|u|^{2_s^*(b) - 2} u}{|x|^{b}} + \lambda f (x, u ), \quad \text{in } \mathbb{R}^N, \end{equation*} where $N > 2 s $, $ 0< s< 1 $, $ \gamma, \lambda $ are real parameters, $(- \Delta)^s$ is the fractional Laplace operator, $2_s^*(b) = {2 (N - b)}/(N - 2s)$ is a critical Hardy-Sobolev exponent with $b \in [0, 2s)$ and $ f \in C(\mathbb R^{N} \times \mathbb{R}, \mathbb{R})$.
Citation
Somayeh Rastegarzadeh. Nemat Nyamoradi. "Existence of positive solutions for Hardy nonlocal fractional elliptic equations involving critical nonlinearities." Topol. Methods Nonlinear Anal. 53 (2) 731 - 746, 2019. https://doi.org/10.12775/TMNA.2019.021