Normalized Ground State Solutions of Nonlinear Schrodinger Equations Involving Exponential Critical Growth

被引：22

作者：

Chang, Xiaojun ^{[1
]}

Liu, Manting ^{[1
]}

Yan, Duokui ^{[2
]}

机构：

[1] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Normalized ground state solutions; Nonlinear Schrodinger equations; Exponential critical growth; Constrained minimization method; Trudinger-Moser inequality; EXISTENCE;

D O I：

10.1007/s12220-022-01130-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with the following nonlinear Schrodinger equation: u +.u = f (u) in R2, u. H1(R2), R2 u2dx =., where. > 0 is given,.. R arises as a Lagrange multiplier and f satisfies an exponential critical growth. Without assuming the Ambrosetti-Rabinowitz condition, we show the existence of normalized ground state solutions for any. > 0. The proof is based on a constrained minimization method and the Trudinger-Moser inequality in R2.

引用

页数：20

共 31 条

[1] Partially coherent solitons on a finite background [J].

Akhmediev, N ;

Ankiewicz, A .

PHYSICAL REVIEW LETTERS, 1999, 82 (13) :2661-2664

[2]

Alves CO, 2022, CALC VAR PARTIAL DIF, V61, DOI 10.1007/s00526-021-02123-1

[3] Existence of a ground state solution for a nonlinear scalar field equation with critical growth [J].

Alves, Claudianor O. ;

Souto, Marco A. S. ;

Montenegro, Marcelo .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2012, 43 (3-4) :537-554

[4]

Alves CO., 2021, arXiv

[5]

[Anonymous], 1997, Minimax Theorems

[6]

[Anonymous], 1993, Duality and perturbation methods in critical point theory

[7] MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION [J].

Bao, Weizhu ;

Cai, Yongyong .

[8] A natural constraint approach to normalized solutions of nonlinear Schrodinger equations and systems (vol 272, pg 4998, 2017) [J].

Bartsch, Thomas ;

Soave, Nicola .

JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (02) :516-521

[9] A natural constraint approach to normalized solutions of nonlinear Schrodinger equations and systems [J].

Bartsch, Thomas ;

Soave, Nicola .

JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (12) :4998-5037

[10] Normalized solutions of nonlinear Schrodinger equations [J].

Bartsch, Thomas ;

de Valeriola, Sebastien .

ARCHIV DER MATHEMATIK, 2013, 100 (01) :75-83

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