Normalized solutions of mass supercritical Schrödinger equations with potential

This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation in the mass supercritical and Sobolev subcritical case We prove the existence of a solution with prescribed L 2 -norm under various conditions on the potential positive and vanishing at infinity,...

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Published inCommunications in partial differential equations Vol. 46; no. 9; pp. 1729 - 1756
Main Authors Bartsch, Thomas, Molle, Riccardo, Rizzi, Matteo, Verzini, Gianmaria
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.09.2021
Taylor & Francis Ltd
Subjects
min-max methods
Nonlinear Schrödinger equations
normalized solution
Schrodinger equation
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Summary:This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation in the mass supercritical and Sobolev subcritical case We prove the existence of a solution with prescribed L 2 -norm under various conditions on the potential positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2021.1893747