Solution curves for semilinear equations on a ball

被引：34

作者：

Korman, P

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1997年 / 125卷 / 07期

关键词：

Dirichlet problem on a ball; Crandall-Rabinowitz theorem;

D O I：

10.1090/S0002-9939-97-04119-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the set of positive solutions of semilinear Dirichlet problem on a ball of radius R in R-n Delta u + lambda f(u) = 0 for \x\<R, u = 0 on \x\ = R consists of smooth curves. Our results can be applied to compute the direction of bifurcation. We also give an easy proof of a uniqueness theorem due to Smeller and Wasserman (1984).

引用

收藏

页码：1997 / 2005

页数：9

相关论文

共 12 条

[1]

CRANDALL MG, 1973, ARCH RATION MECH AN, V52, P161, DOI 10.1007/BF00282325

[2] ON THE STRUCTURE OF SOLUTIONS OF AN EQUATION IN CATALYSIS THEORY WHEN A PARAMETER IS LARGE [J].

DANCER, EN .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1980, 37 (03) :404-437

[3]

EVANS LC, 1994, BERKELEY ECT NOTES M, V3

[4] THE SET OF POSITIVE SOLUTIONS OF SEMILINEAR EQUATIONS IN LARGE BALLS [J].

GARDNER, R ;

PELETIER, LA .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1986, 104 :53-72

[5] SYMMETRY AND RELATED PROPERTIES VIA THE MAXIMUM PRINCIPLE [J].

GIDAS, B ;

NI, WM ;

NIRENBERG, L .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 68 (03) :209-243

[6] UNIQUENESS OF GLOBAL POSITIVE SOLUTION BRANCHES OF NONLINEAR ELLIPTIC PROBLEMS [J].

HOLZMANN, M ;

KIELHOFER, H .

MATHEMATISCHE ANNALEN, 1994, 300 (02) :221-241

[7] Exact multiplicity results for boundary value problems with nonlinearities generalising cubic [J].

Korman, P ;

Li, Y ;

Ouyang, T .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 :599-616

[8]

KORMAN P, IN PRESS FUNKCIALAJ

[9]

KORMAN P, INP RESS COMM PDE

[10] A COUNTEREXAMPLE TO THE NODAL DOMAIN CONJECTURE AND A RELATED SEMILINEAR EQUATION [J].

LIN, CS ;

NI, WM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 102 (02) :271-277