A CLASS OF GENERALIZED QUASILINEAR SCHRODINGER EQUATIONS

被引：28

作者：

Shen, Yaotian ^{[1
]}

Wang, Youjun ^{[1
]}

机构：

[1] S China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 03期

关键词：

Quasilinear Schrodinger equations; critical exponents; generalized; SOLITON-SOLUTIONS; POSITIVE SOLUTIONS; GROUND-STATE; EXISTENCE;

D O I：

10.3934/cpaa.2016.15.853

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence of nontrivial solutions for the following quasilinear Schrodinger equation with critical Sobolev exponent: -Delta u + V(x)u - Delta[l(u(2))]l'(u(2))u = lambda u(alpha 2* 1) + h(u), x epsilon R-N, where V(x) : R-N -> R is a given potential and l, h are real functions, lambda >= 0, alpha > 1, 2* = 2N/(N - 2), N >= 3. Our results cover two physical models l(s) = s(alpha/2) and l(s) = (1 + s)(alpha/2) with alpha >= 3/2.

引用

页码：853 / 870

页数：18

共 29 条

[1] Uniqueness of the ground state solutions of quasilinear Schrodinger equations [J].

Adachi, Shinji ;

Watanabe, Tatsuya .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (02) :819-833

[2]

Adachi S, 2011, ADV DIFFERENTIAL EQU, V16, P289

[3]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[4]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[5] Soliton solutions for quasilinear Schrodinger equations with critical growth [J].

Bezerra do O, Joao M. ;

Miyagaki, Olimpio H. ;

Soares, Sergio H. M. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (04) :722-744

[6] 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

[7] Static solutions of a D-dimensional modified nonlinear Schrodinger equation [J].

Brizhik, L ;

Eremko, A ;

Piette, B ;

Zakrzewski, WJ .

NONLINEARITY, 2003, 16 (04) :1481-1497

[8] Solutions for a quasilinear Schrodinger equation: a dual approach [J].

Colin, M ;

Jeanjean, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (02) :213-226

[9] Global existence of small solutions to a relativistic nonlinear Schrodinger equation [J].

deBouard, A ;

Hayashi, N ;

Saut, JC .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 189 (01) :73-105

[10] Electrons on hexagonal lattices and applications to nanotubes [J].

Hartmann, B ;

Zakrzewski, WJ .

PHYSICAL REVIEW B, 2003, 68 (18)

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