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

被引：73

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 50 条

[1] Lane-Emden-Fowler equations with convection and singular potential
Dupaigne, Louis
Ghergu, Marius
Radulescu, Vicentiu
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (06): : 563 - 581
[2] A Lane-Emden-Fowler type problem with singular nonlinearity
Covei, Dragos-Patru
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2009, 49 (02): : 325 - 338
[3] APPROXIMATE ANALYTICAL SOLUTIONS OF GENERALIZED LANE-EMDEN-FOWLER EQUATIONS
Vassilev, Vassil M.
Dantchev, Daniel M.
Popov, Svilen, I
PROCEEDINGS OF THE TWENTY-FIRST INTERNATIONAL CONFERENCE ON GEOMETRY, INTEGRABILITY AND QUANTIZATION, 2020, 21 : 302 - 309
[4] Solving the Lane-Emden-Fowler Type Equations of Higher Orders by the Adomian Decomposition Method
Wazwaz, Abdul-Majid
Rach, Randolph
Bougoffa, Lazhar
Duan, Jun-Sheng
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2014, 100 (06): : 507 - 529
[5] Bifurcation and asymptotics for the Lane-Emden-Fowler equation
Ghergu, M
Radulescu, VD
COMPTES RENDUS MATHEMATIQUE, 2003, 337 (04) : 259 - 264
[6] A REMARK ON GROUND STATE SOLUTIONS FOR LANE-EMDEN-FOWLER EQUATIONS WITH A CONVECTION TERM
Xue, Hongtao
Zhang, Zhijun
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[7] The supercritical Lane-Emden-Fowler equation in exterior domains
Davila, Juan
del Pino, Manuel
Muss, Monica
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1225 - 1243
[8] Effective computation of exact and analytic approximate solutions to singular nonlinear equations of Lane-Emden-Fowler type
Turkyilmazoglu, M.
APPLIED MATHEMATICAL MODELLING, 2013, 37 (14-15) : 7539 - 7548
[9] RADIAL SOLUTIONS OF LANE-EMDEN-FOWLER EQUATIONS WITH PUCCI'S EXTREMAL OPERATORS
Leoni, Fabiana
BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, 2019, 10 : 1 - 13
[10] A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations
Zhai, Chengbo
Anderson, Douglas R.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 375 (02) : 388 - 400

← 1 2 3 4 5 →