Singular perturbed problems in the zero mass case: asymptotic behavior of spikes

被引：12

作者：

Dancer, E. N. ^{[1
]}

Santra, Sanjiban ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2010年 / 189卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

Concentration phenomena; Peak solutions; Morse index; Finite dimensional reduction; NONLINEAR SCHRODINGER-EQUATIONS; SEMILINEAR NEUMANN PROBLEM; LEAST-ENERGY SOLUTIONS; BOUND-STATES; ELLIPTIC-EQUATIONS; EXISTENCE; LOCATION; SHAPE;

D O I：

10.1007/s10231-009-0105-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the asymptotic behavior of the least energy solution of a Dirichlet problem in the zero mass case. If Q is a uniformly positive potential having k isolated local minima, then we prove the existence of a positive multi-spike solutions having k peaks concentrating at each local minima of the potential.

引用

页码：185 / 225

页数：41

共 19 条

[1] Pure and mixed phase Bi2O3 thin films obtained by metal organic chemical vapor deposition [J].

Bandoli, G ;

Barreca, D ;

Brescacin, E ;

Rizzi, GA ;

Tondello, E .

CHEMICAL VAPOR DEPOSITION, 1996, 2 (06) :238-&

[2]

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

[3]

Dancer E. N., 1995, TOPOL METHOD NONL AN, V5, P141

[4] SOME NOTES ON THE METHOD OF MOVING PLANES [J].

DANCER, EN .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1992, 46 (03) :425-434

[5] Multi-peak bound states for nonlinear Schrodinger equations [J].

Del Pino, M ;

Felmer, PL .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1998, 15 (02) :127-149

[6] Semi-classical states for nonlinear Schrodinger equations [J].

delPino, M ;

Felmer, PL .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 149 (01) :245-265

[7] Local mountain passes for semilinear elliptic problems in unbounded domains [J].

delPino, M ;

Felmer, PL .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1996, 4 (02) :121-137

[8] NONSPREADING WAVE-PACKETS FOR THE CUBIC SCHRODINGER-EQUATION WITH A BOUNDED POTENTIAL [J].

FLOER, A ;

WEINSTEIN, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1986, 69 (03) :397-408

[9] Asymptotic shape and location of small cores in elliptic free-boundary problems [J].

Flucher, M ;

Wei, J .

MATHEMATISCHE ZEITSCHRIFT, 1998, 228 (04) :683-703

[10]

Gidas B., 1981, Commun. Partial Differ. Equ., V6, P883, DOI 10.1080/03605308108820196

← 1 2 →