Existence of normalized solutions for the Schrodinger equation

被引：5

作者：

Deng, Shengbing ^{[1
]}

Wu, Qiaoran ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

COMMUNICATIONS IN ANALYSIS AND MECHANICS | 2023年 / 15卷 / 03期

关键词：

normalized solutions; Schrodinger equation; Sobolev critical nonlinearities; approximation method; mountain-pass type solution;

D O I：

10.3934/cam.2023028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we devote to studying the existence of normalized solutions for the following Schr <spacing diaeresis>odinger equation with Sobolev critical nonlinearities. ( u = u +R ju jq 2u + ju j p 2u in R N; RN juj2dx = a2; where N > 3, 2 < q < 2 + 4N, p = 2 = 2N N 2, a; > 0 and 2 R is a Lagrange multiplier. Since the existence result for 2 + 4N < p < 2 has been proved, using an approximation method, that is let p ! 2 , we obtain that there exists a mountain-pass type solution for p = 2.

引用

页码：575 / 585

页数：11

共 22 条

[1] 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

[2] Entropy solutions for elliptic Schrodinger type equations under Fourier boundary conditions [J].

Benboubker, Mohamed Badr ;

Benkhalou, Hayat ;

Hjiaj, Hassane ;

Nyanquini, Ismael .

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2023, 72 (04) :2831-2855

[3] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[4] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].

BREZIS, H ;

LIEB, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490

[5] THE CAUCHY-PROBLEM FOR THE CRITICAL NONLINEAR SCHRODINGER-EQUATION IN HS [J].

CAZENAVE, T ;

WEISSLER, FB .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 14 (10) :807-836

[6] Existence of solutions with prescribed norm for semilinear elliptic equations [J].

Jeanjean, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (10) :1633-1659

[7] Multiple normalized solutions for a Sobolev critical Schrodinger equation [J].

Jeanjean, Louis ;

Thanh Trung Le .

MATHEMATISCHE ANNALEN, 2022, 384 (1-2) :101-134

[8] Infinitely many solutions for quasilinear Schrodinger equations with sign-changing nonlinearity without the aid of 4-superlinear at infinity [J].

Khiddi, Mustapha ;

Essafi, Lakbir .

DEMONSTRATIO MATHEMATICA, 2022, 55 (01) :831-842

[9] Normalized solutions for a coupled fractional Schrodinger system in low dimensions [J].

Li, Meng ;

He, Jinchun ;

Xu, Haoyuan ;

Yang, Meihua .

BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)

[10] Existence of normalized ground states for the Sobolev critical Schrodinger equation with combined nonlinearities [J].

Li, Xinfu .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (05)

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