Flat Solutions of Some Non-Lipschitz Autonomous Semilinear Equations May be Stable for N ≥ 3

被引：11

作者：

Ildefonso Diaz, Jesus ^{[1
]}

Hernandez, Jesus ^{[2
]}

Il'yasov, Yavdat ^{[3
]}

机构：

[1] Univ Complutense Madrid, Inst Matemat Interdisciplinar, E-28040 Madrid, Spain

[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[3] RAS, Inst Math, Ufa Sci Ctr, 112 Chernyshevsky Str, Ufa 450077, Russia

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2017年 / 38卷 / 01期

关键词：

Semilinear elliptic and parabolic equation; Strong absorption; Spectral problem; Nehari manifolds; Pohozaev identity; Flat solution; Linearized stability; Lyapunov function; Global instability; ELLIPTIC PROBLEM; EXISTENCE; PRINCIPLE; SYMMETRY; SUPPORT;

D O I：

10.1007/s11401-016-1073-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The authors prove that flat ground state solutions (i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1,2 and they can be stable for N >= 3 for suitable values of the involved exponents.

引用

页码：345 / 378

页数：34

共 53 条

[1]

Akagi G., COMMUNICATI IN PRESS

[2] ON THE RETENTION OF THE INTERFACES IN SOME ELLIPTIC AND PARABOLIC NONLINEAR PROBLEMS [J].

Alvarez, Luis ;

Ildefonso Diaz, Jesus .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (01) :1-17

[3]

[Anonymous], 1990, Differential and Integral Equations

[4]

[Anonymous], 1975, ANN SCUOLA NORM-SCI

[5]

[Anonymous], 1973, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

[6]

[Anonymous], 1996, VARIATIONAL METHODS, DOI DOI 10.1007/978-3-662-03212-1

[7]

[Anonymous], 1992, PITMAN RES NOTES MAT

[8]

[Anonymous], 1996, Advances in Diff. Equs.

[9]

[Anonymous], UNPUB

[10]

[Anonymous], COMM PARTIAL DIFFERE

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