ON THE LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR A NONLINEAR ELLIPTIC SYSTEM

被引：18

作者：

Sato, Yohei ^{[1
]}

Wang, Zhi-Qiang ^{[2
,3
,4
]}

机构：

[1] Osaka City Univ, Grad Sch Sci, Adv Math Inst, Smiyoshi Ku, Osaka 5588585, Japan

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[4] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 05期

关键词：

Nonlinear Schrodinger system; sign-changing solutions; multiple existence of solutions; least energy solution; BOUND-STATES; SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS; GROUND-STATES; WAVES;

D O I：

10.3934/dcds.2015.35.2151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, as bound state solutions we consider least energy sign-changing solutions to a nonlinear elliptic system which consists of N-equations defined on a bounded domain Q. For any subset K subset of {1, ... , N}, we show the existence of sign-changing solution (u) over right arrow = (u(1), ... , u(n)) such that, for i is an element of K, u(i) are sign-changing functions that change sign exactly once in Omega, and, for i is not an element of K, u(i) are one sign functions. We give a variational characterization of such solutions on modified Nehari type constrained sets.

引用

页码：2151 / 2164

页数：14

共 26 条

[1] Multi-bump solitons to linearly coupled systems of nonlinear Schrodinger equations [J].

Ambrosetti, A. ;

Colorado, E. ;

Ruiz, D. .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2007, 30 (01) :85-112

[2] Standing waves of some coupled nonlinear Schrodinger equations [J].

Ambrosetti, Antonio ;

Colorado, Eduardo .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2007, 75 :67-82

[3] Bound states for a coupled Schrodinger system [J].

Bartsch, Thomas ;

Wang, Zhi-Qiang ;

Wei, Juncheng .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2007, 2 (02) :353-367

[4]

Bartsch T, 2006, J PARTIAL DIFFER EQ, V19, P200

[5] A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system [J].

Bartsch, Thomas ;

Dancer, E. Norman ;

Wang, Zhi-Qiang .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) :345-361

[6] A sign-changing solution for a superlinear Dirichlet problem [J].

Castro, A ;

Cossio, J ;

Neuberger, JM .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1997, 27 (04) :1041-1053

[7] Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates [J].

Chang, SM ;

Lin, CS ;

Lin, TC ;

Lin, WW .

PHYSICA D-NONLINEAR PHENOMENA, 2004, 196 (3-4) :341-361

[8] Nehari's problem and competing species systems [J].

Conti, M ;

Terracini, S ;

Verzini, G .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2002, 19 (06) :871-888

[9] A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system [J].

Dancer, E. N. ;

Wei, Juncheng ;

Weth, Tobias .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (03) :953-969

[10] Spike's in two coupled nonlinear Schrodinger equations [J].

Lin, TC ;

Wei, JC .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2005, 22 (04) :403-439

← 1 2 3 →