Detail publikace

NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R2

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

Originální název

NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R2

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

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

Vydáno

20. 12. 2023

Nakladatel

SIAM PUBLICATIONS

Místo

PHILADELPHIA

ISSN

0036-1410

Periodikum

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Ročník

55

Číslo

6

Stát

Spojené státy americké

Strany od

7704

Strany do

7740

Strany počet

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"
}