Liouville theorems for stable radial solutions for the biharmonic operator

被引：15

作者：

Warnault, Guillaume ^{[1
]}

机构：

[1] Univ Tours, CNRS, LMPT, UMR 6083, F-37200 Tours, France

来源：

ASYMPTOTIC ANALYSIS | 2010年 / 69卷 / 1-2期

关键词：

biharmonic operator; Liouville result; SEMILINEAR ELLIPTIC-EQUATIONS; R-N; CLASSIFICATION;

D O I：

10.3233/ASY-2010-0997

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with the non-existence of stable solutions for a fourth-order semilinear elliptic equation Delta(2)u = f(u) in R(N), where f is a smooth nonlinearity. We establish the non-existence of stable radial solutions which verify decay conditions at infinity. Our Liouville-type results do not depend on the specific nonlinearity f. Moreover, in low dimensions and under no radial symmetry assumption, we prove Liouville-type results when f is increasing.

引用

页码：87 / 98

页数：12

共 11 条

[1] On the stability of radial solutions of semilinear elliptic equations in all of Rn [J].

Cabré, X ;

Capella, A .

COMPTES RENDUS MATHEMATIQUE, 2004, 338 (10) :769-774

[2]

De Figueiredo D.G., 1994, Ann. Sc. Norm. Sup. Pisa, V21, P387

[3] Liouville theorems for stable solutions of semilinear elliptic equations with convex nonlinearities [J].

Dupaigne, L. ;

Farina, A. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (08) :2882-2888

[4]

DUPAIGNE L, STABLE SOLUTIONS DEL

[5] 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

[6] Stable solutions of -Δu = eu on RN [J].

Farina, Alberto .

COMPTES RENDUS MATHEMATIQUE, 2007, 345 (02) :63-66

[7]

Farina A, 2008, ANN SCUOLA NORM-SCI, V7, P741

[8]

Souto M. A., 1992, THESIS UNICAMP

[9] Asymptotic behavior of stable radial solutions of semilinear elliptic equations in RN [J].

Villegas, Salvador .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 88 (03) :241-250

[10] REGULARITY OF THE EXTREMAL SOLUTION FOR A BIHARMONIC PROBLEM WITH GENERAL NONLINEARITY [J].

Warnault, Guillaume .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (05) :1709-1723

← 1 2 →