Ground state solutions of Hamiltonian elliptic systems in dimension two

被引：16

作者：

de Figueiredo, Djairo G. ^{[1
]}

do O, Joao Marcos ^{[2
]}

Zhang, Jianjun ^{[3
]}

机构：

[1] Univ Estadual Campinas, IMECC, CP 6065, BR-13081970 Campinas, SP, Brazil

[2] Univ Fed Paraiba, BR-58051900 Joao Pessoa, Paraiba, Brazil

[3] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2020年 / 150卷 / 04期

关键词：

Hamiltonian elliptic system; Trudinger-Moser inequality; ground state; generalized Nehari manifold; POSITIVE SOLUTIONS; EQUATIONS; EXISTENCE; GROWTH; INEQUALITIES; R-2;

D O I：

10.1017/prm.2018.78

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to study Hamiltonian elliptic system of the form where Omega subset of R-2 is a bounded domain. In the second place, we present existence results for the following stationary Schrodinger systems defined in the whole plane We assume that the nonlinearities f, g have critical growth in the sense of Trudinger Moser. By using a suitable variational framework based on the generalized Nehari manifold method, we obtain the existence of ground state solutions of both systems (0.1) and (0.2).

引用

页码：1737 / 1768

页数：32

共 42 条

[1] Trudinger type inequalities in RN and their best exponents [J].

Adachi, S ;

Tanaka, K .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (07) :2051-2057

[2] On a class of Hamiltonian elliptic systems involving unbounded or decaying potentials in dimension two [J].

Albuquerque, Francisco S. B. ;

do O, Joao Marcos ;

Medeiros, Everaldo S. .

MATHEMATISCHE NACHRICHTEN, 2016, 289 (13) :1568-1584

[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]

[Anonymous], 1997, Abstr. Appl. Anal.

[5]

[Anonymous], 2010, The Method of Nehari Manifold, Handbook of Nonconvex Analysis and Applications

[6]

[Anonymous], J DIFFER EQU

[7] CRITICAL-POINT THEOREMS FOR INDEFINITE FUNCTIONALS [J].

BENCI, V ;

RABINOWITZ, PH .

INVENTIONES MATHEMATICAE, 1979, 52 (03) :241-273

[8] Hamiltonian elliptic systems: a guide to variational frameworks [J].

Bonheure, D. ;

Moreira dos Santos, E. ;

Tavares, H. .

PORTUGALIAE MATHEMATICA, 2014, 71 (3-4) :301-395

[9]

Bonheure D, 2012, T AM MATH SOC, V364, P447

[10] 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

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