Pohozaev method and nontrivial ground state solutions for a class of quasilinear Schrödinger system

被引：0

作者：

Zhang, Zaiyun ^{[1
]}

Chen, Jiannan ^{[1
]}

Chen, Yongqi ^{[1
]}

Liu, Jie ^{[1
]}

Yang, Yu ^{[1
]}

机构：

[1] Hunan Inst Sci & Technol, Sch Math, Yueyang 414006, Hunan, Peoples R China

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2025年 / 27卷 / 01期

关键词：

Quasilinear Schr & ouml; dinger system; nontrivial ground state solution; Poho & zcaron; aev manifold; Moser iteration; NONLINEAR SCHRODINGER-EQUATIONS; SIGN-CHANGING SOLUTIONS; SEMICLASSICAL STATES; ELLIPTIC-EQUATIONS; SOLITON-SOLUTIONS; NODAL SOLUTIONS; EXISTENCE;

D O I：

10.1007/s11784-024-01156-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the following quasilineat Schr & ouml;dinger system in the entire space R-N 11. M. -Delta uj+uj+tau 2 Delta(u2j)uj=M & sum;k=1ajk|uk|p+1|uj|p-1uj,j=1,...,M, where N >= 3,0 <p<> 0 is a parameter and ajk are positive real numbers. Using the Pohozaev manifold approach and Moser iteration technique, we demonstrate the existence of the nontrivial ground state solutions.

引用

页数：21

共 43 条

[1] Blow-up phenomena and asymptotic profiles of ground states of quasilinear elliptic equations with H1-supercritical nonlinearities [J].

Adachi, Shinji ;

Shibata, Masataka ;

Watanabe, Tatsuya .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (04) :1492-1514

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

Akhmediev, N ;

Ankiewicz, A .

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

[3] Soliton solutions for a class of quasilinear Schrodinger equations with a parameter [J].

Alves, Claudianor O. ;

Wang, Youjun ;

Shen, Yaotian .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (01) :318-343

[4]

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

[5]

Borovskii A. V., 1993, Journal of Experimental and Theoretical Physics, V77, P562

[6] RELATIVISTIC AND PONDEROMOTIVE SELF-FOCUSING OF A LASER-BEAM IN A RADIALLY INHOMOGENEOUS-PLASMA .1. PARAXIAL APPROXIMATION [J].

BRANDI, HS ;

MANUS, C ;

MAINFRAY, G ;

LEHNER, T ;

BONNAUD, G .

PHYSICS OF FLUIDS B-PLASMA PHYSICS, 1993, 5 (10) :3539-3550

[7] 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

[8] Bifurcation analysis for a modified quasilinear equation with negative exponent [J].

Chen, Siyu ;

Santos, Carlos Alberto ;

Yang, Minbo ;

Zhou, Jiazheng .

ADVANCES IN NONLINEAR ANALYSIS, 2022, 11 (01) :684-701

[9] Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent [J].

Chen, Zhijie ;

Zou, Wenming .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 205 (02) :515-551

[10] Characterization of ground-states for a system of M coupled semilinear Schrodinger equations and applications [J].

Correia, Simao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (04) :3302-3326

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