Publication detail

NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R2

CHEN, S. RADULESCU, V. TANG, X. SHUAI, Y.

Original Title

NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R2

Type

journal article in Web of Science

Language

English

Original Abstract

For any a > 0, we study the existence of normalized solutions and ground state solutions to the following Schrodinger equation with L-2-constraint: { -Delta u + lambda u = b(x)f(u) x is an element of R-2, integral(2)(R) u(2)dx = a, where lambda is an element of R is a Lagrange multiplier, the potential b is an element of C(R-2, (0, infinity)) satisfies 0 < lim(|y|->infinity) b(y) <= inf(x is an element of)R(2) b(x) and appears as a converse direction of the Rabinowitz-type trapping potential, and the reaction f is an element of C(R, R) enjoys critical exponential growth of Trudinger-Moser type. Under two different kinds of assumptions on f, we prove several new existence results, which, in the context of normalized solutions, can be considered as both counterparts of planar unconstrained critical problems and extensions of unconstrained Schrodinger problems with Rabinowitz-type trapping potential. Especially, in this scenario, we develop some sharp estimates of energy levels and ingenious analysis techniques to restore the compactness which are novel even for b(x) equivalent to constant. We believe that these techniques will allow not only treating other L-2-constrained problems in the Trudinger-Moser critical setting but also generalizing previous results to the case of variable potentials.

Keywords

Schrodinger equation; normalized solution; critical exponential growth; Trudinger-Moser inequality

Authors

CHEN, S.; RADULESCU, V.; TANG, X.; SHUAI, Y.

Released

20. 12. 2023

Publisher

SIAM PUBLICATIONS

Location

PHILADELPHIA

ISBN

0036-1410

Periodical

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Year of study

55

Number

6

State

United States of America

Pages from

7704

Pages to

7740

Pages count

37

URL

https://epubs.siam.org/doi/10.1137/22M1521675

BibTex

@article{BUT187393,
  author="Sitong {Chen} and Vicentiu {Radulescu} and Xianhua {Tang} and Yuan {Shuai}",
  title="NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R2",
  journal="SIAM JOURNAL ON MATHEMATICAL ANALYSIS",
  year="2023",
  volume="55",
  number="6",
  pages="7704--7740",
  doi="10.1137/22M1521675",
  issn="0036-1410",
  url="https://epubs.siam.org/doi/10.1137/22M1521675"
}