The existence and multiplicity of the normalized solutions for fractional Schrödinger equations involving Sobolev critical exponent in the L2-subcritical and L2-supercritical cases

This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: where , , , , and . We consider the -subcritical and -supercritical cases. More precisely, in -subcritical case, we obtain the multiplicity of the normal...

Full description

Saved in:
Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 11; no. 1; pp. 1531 - 1551
Main Authors Li, Quanqing, Zou, Wenming
Format Journal Article
LanguageEnglish
Published De Gruyter 23.05.2022
Subjects
35J20
35J50
35J70
l2-subcritical
l2-supercritical
normalized solutions
Sobolev critical exponent
subcritical
supercritical
Online AccessGet full text

Cover

More Information
Summary:This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: where , , , , and . We consider the -subcritical and -supercritical cases. More precisely, in -subcritical case, we obtain the multiplicity of the normalized solutions for problem by using the truncation technique, concentration-compactness principle, and genus theory. In -supercritical case, we obtain a couple of normalized solution for by using a fiber map and concentration-compactness principle. To some extent, these results can be viewed as an extension of the existing results from Sobolev subcritical growth to Sobolev critical growth.
ISSN:2191-950X
DOI:10.1515/anona-2022-0252