Liouville results for m-Laplace equations of Lane-Emden-Fowler type

被引：77

作者：

Damascelli, Lucio ^{[2
]}

Farina, Alberto ^{[1
]}

Sciunzi, Berardino ^{[3
]}

Valdinoci, Enrico ^{[2
]}

机构：

[1] Univ Picardie, LAMFA, CNRS UMR 6140, Fac Math & Informat, F-80039 Amiens 1, France

[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[3] Univ Calabria, Dipartimento Matemat, VP Bucci, Arcavacata Di Rende, CS, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 04期

关键词：

Degenerate PDEs; Stable solutions; Critical exponents; Rigidity results; DEGENERATE ELLIPTIC-EQUATIONS; STRONG MAXIMUM PRINCIPLE; POSITIVE SOLUTIONS; UNBOUNDED-DOMAINS; LOCAL BEHAVIOR; R-N; REGULARITY; CLASSIFICATION; IDENTITY;

D O I：

10.1016/j.anihpc.2008.06.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider sign changing solutions of the equation -Delta(m)(u) = |u|(p-1) u in possibly unbounded domains or in R-N. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for in > 2 and in - 1 < P < pc(N, m). Here pc(N, m) is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one. (C) 2008 Elsevier Masson SAS. All rights reserved.

引用

页码：1099 / 1119

页数：21

共 28 条

[1]

[Anonymous], 2000, Differ. Integral. Equ

[2]

[Anonymous], 1931, Q. J. Math, DOI [10.1093/qmath/os-2.1.259, DOI 10.1093/QMATH/OS-2.1.259]

[3] LOCAL AND GLOBAL BEHAVIOR OF SOLUTIONS OF QUASILINEAR EQUATIONS OF EMDEN-FOWLER TYPE [J].

BIDAUTVERON, MF .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1989, 107 (04) :293-324

[4] NONLINEAR ELLIPTIC-EQUATIONS ON COMPACT RIEMANNIAN-MANIFOLDS AND ASYMPTOTICS OF EMDEN EQUATIONS [J].

BIDAUTVERON, MF ;

VERON, L .

INVENTIONES MATHEMATICAE, 1991, 106 (03) :489-539

[5] Degenerate elliptic equations with singular nonlinearities [J].

Castorina, Daniele ;

Esposito, Pierpaolo ;

Sciunzi, Berardino .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (03) :279-306

[6] CLASSIFICATION OF SOLUTIONS OF SOME NONLINEAR ELLIPTIC-EQUATIONS [J].

CHEN, WX ;

LI, CM .

DUKE MATHEMATICAL JOURNAL, 1991, 63 (03) :615-622

[7] Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations [J].

Damascelli, L ;

Sciunzi, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 206 (02) :483-515

[8] Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-laplace equations [J].

Damascelli, L ;

Sciunzi, B .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 25 (02) :139-159

[9]

Damascelli L., 2001, Adv. Nonlinear Stud, V1, P40

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

DANCER, EN .

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

← 1 2 3 →