Bifurcation and admissible solutions for the Hessian equation

被引：31

作者：

Dai, Guowei ^{[1
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 273卷 / 10期

关键词：

Bifurcation; Admissible solution; Hessian equation; DIRICHLET PROBLEM; POSITIVE SOLUTIONS; ISOPERIMETRIC-INEQUALITIES; ELLIPTIC-EQUATIONS; EXACT MULTIPLICITY; EIGENVALUES; DIMENSION; BRANCH;

D O I：

10.1016/j.jfa.2017.08.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the following eigenvalue problem of k-Hessian equation { S-k(D(2)u) = lambda(k)f(-u) in B, u= 0 on partial derivative B. Global bifurcation result is established for this problem. As applications of the bifurcation result, we determine the intervals of A for the existence, nonexistence, uniqueness and multiplicity of radially symmetric k-admissible solutions for this problem. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：3200 / 3240

页数：41

共 48 条

[1] Admas R.A., 1975, Sobolev Spaces
[2] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES
AMANN, H
[J]. SIAM REVIEW, 1976, 18 (04) : 620 - 709
[3] Ambrosetti A., 1990, Comment. Math. Univ. Carol, V31, P213
[4] AMICK CJ, 1988, J REINE ANGEW MATH, V384, P1
[5] [Anonymous], CAMBRIDGE STUDIES AD
[6] [Anonymous], 1973, MATH STUD
[7] [Anonymous], 1985, NONLINEAR FUNCTIONAL
[8] S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology
Arcoya, D
Diaz, JI
Tello, L
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 150 (01) : 215 - 225
[9] Berestycki H., 1980, Lecture Notes in Math., V782, P16
[10] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN
CAFFARELLI, L
NIRENBERG, L
SPRUCK, J
[J]. ACTA MATHEMATICA, 1985, 155 (3-4) : 261 - 301

← 1 2 3 4 5 →