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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

Authors
  • Ho, Ky1
  • Kim, Yun-Ho2
  • 1 Institute of Applied Mathematics, University of Economics Ho Chi Minh City, 59C, Nguyen Dinh Chieu Street, District 3 , (Vietnam)
  • 2 Department of Mathematics Education, Sangmyung University, 03016 , (South Korea)
Type
Published Article
Journal
Advances in Nonlinear Analysis
Publisher
De Gruyter
Publication Date
Dec 08, 2020
Volume
10
Issue
1
Pages
816–848
Identifiers
DOI: 10.1515/anona-2020-0160
Source
De Gruyter
Keywords
License
Green

Abstract

We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.

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