ON FINITE MORSE INDEX SOLUTIONS OF HIGHER ORDER FRACTIONAL LANE-EMDEN EQUATIONS

被引：31

作者：

Fazly, Mostafa ^{[1
]}

Wei, Juncheng

机构：

[1] Univ Texas San Antonio, Dept Math, San Antonio, TX 78249 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2017年 / 139卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

R-N; CLASSIFICATION; LAPLACIAN;

D O I：

10.1353/ajm.2017.0011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify finite Morse index solutions of the following nonlocal Lane-Emden equation (-Delta)(s)u = vertical bar u vertical bar(p-1)u R-n for 1 < s < 2 via a novel monotonicity formula. For local cases s = 1 and s = 2 this classification was provided by Farina in 2007 and Davila, Dupaigne, Wang, and Wei in 2014, respectively. Moreover, for the nonlocal case 0 < s < 1 finite Morse index solutions are classified by Davila, Dupaigne, and Wei in their 2014 preprint.

引用

页码：433 / 460

页数：28

共 21 条

[1] ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH [J].

CAFFARELLI, LA ;

GIDAS, B ;

SPRUCK, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (03) :271-297

[2] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[3] On Fractional GJMS Operators [J].

Case, Jeffrey S. ;

Chang, Sun-Yung Alice .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2016, 69 (06) :1017-1061

[4] Fractional Laplacian in conformal geometry [J].

Chang, Sun-Yung Alice ;

del Mar Gonzalez, Maria .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1410-1432

[5] Classification of solutions for an integral equation [J].

Chen, WX ;

Li, CM ;

Ou, B .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2006, 59 (03) :330-343

[6]

Davila J., PREPRINT

[7] A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem [J].

Davila, Juan ;

Dupaigne, Louis ;

Wang, Kelei ;

Wei, Juncheng .

ADVANCES IN MATHEMATICS, 2014, 258 :240-285

[8]

Fall M. M., PREPRINT

[9] On the classification of solutions of the Lane-Emden equation on unbounded domains of RN [J].

Farina, Alberto .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (05) :537-561

[10] Radial entire solutions for supercritical biharmonic equations [J].

Gazzola, F ;

Grunau, HC .

MATHEMATISCHE ANNALEN, 2006, 334 (04) :905-936

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