Lions-type theorem of the fractional Laplacian and applications
type: Item
instance of: scholarly article
title: Lions-type theorem of the fractional Laplacian and applications
zbMATH Open document ID: 1476.35307
author: Yanyan Li
published in: Dynamics of Partial Differential Equations
publication date: 2021-08-23T00:00:00Z
review text: In this paper, the authors study a class of fractional Schrödinger equation \((-\Delta)^su + V(|x|)u = f(u), x\in\mathbb R^N,\) with radially symmetric potential \(V\), and prove a generalized version of Lions-type theorem in the case the nonlinearity \(f\) contains both embedding top and bottom indices. As an application of this theorem, the authors consider the existence of ground state solutions when \(f(u)=|u|^{2^*_s-2}u +\lambda |u|^{q-2}u + |u|^{2^*_{\alpha,s}-2}u,\) and \(2^*_{\alpha,s}=2+\frac{2\alpha}{N-2s}, \alpha\in(0,2s)\).
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 7384143
zbMATH Keywords: Lions theorem
zbMATH Keywords: fractional equation
zbMATH Keywords: singular potential
zbMATH Keywords: Nehari manifold
zbMATH Keywords: ground state solution
reviewed by: Xiaoming He
MaRDI profile type: Publication
Wikidata QID: Q115203500
DOI: 10.4310/DPDE.2021.V18.N3.A3
description: scientific article; zbMATH DE number 7384143