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2019 Existence of positive solutions for Hardy nonlocal fractional elliptic equations involving critical nonlinearities
Somayeh Rastegarzadeh, Nemat Nyamoradi
Topol. Methods Nonlinear Anal. 53(2): 731-746 (2019). DOI: 10.12775/TMNA.2019.021

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})$.

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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

Information

Published: 2019
First available in Project Euclid: 11 May 2019

zbMATH: 07130717
MathSciNet: MR3983992
Digital Object Identifier: 10.12775/TMNA.2019.021

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.53 • No. 2 • 2019
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