Bifurcation from trivial solution for elliptic systems with nonlinear boundary conditions

被引：1

作者：

Zhang, Yang ^{[1
]}

Wang, Mingxin ^{[2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150080, Peoples R China

[2] Harbin Inst Technol, Nat Sci Res Ctr, Harbin 150080, Peoples R China

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2015年 / 60卷 / 07期

关键词：

35J55; 35B32; 35B35; 35J65; bifurcation; elliptic systems; nonlinear boundary conditions; stability; DIFFUSIVE LOGISTIC EQUATIONS; GLOBAL BIFURCATION;

D O I：

10.1080/17476933.2014.985216

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate semilinear elliptic systems having a parameter with nonlinear Neumann boundary conditions over a smooth bounded domain. The objective of our study is to analyse bifurcation component of positive solutions from trivial solution and their stability. The results are obtained via classical bifurcation theorem from a simple eigenvalue, by studying the eigenvalue problem of elliptic systems.

引用

页码：951 / 967

页数：17

共 50 条

[31] STEKLOV SPECTRUM AND NONRESONANCE FOR ELLIPTIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS
Mavinga, Nsoki
Nkashama, Mubenga N.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, : 197 - 205
[32] A nonlinear optimization bifurcation tracking method for periodic solution of nonlinear systems
Liao, Haitao
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES, 2023, 51 (03) : 1201 - 1225
[33] MULTIPLE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS WITH NONLINEAR BOUNDARY CONDITIONS
Nguyen Thanh Chung
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2008,
[34] The existence of positive solutions to an elliptic system with nonlinear boundary conditions
Chunhua Wang
Jing Yang
Boundary Value Problems, 2013
[35] MULTIPLE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS
Harada, Junichi
Otani, Mitsuharu
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
[36] Stability analysis for positive solutions for classes of semilinear elliptic boundary-value problems with nonlinear boundary conditions
Goddard, Jerome, II
Shivaji, Ratnasingham
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2017, 147 (05) : 1019 - 1040
[37] Elliptic p-Laplacian systems with nonlinear boundary condition
Borer, Franziska
Carl, Siegfried
Winkert, Patrick
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 538 (02)
[38] New linking theorem and elliptic systems with nonlinear boundary condition
Zou, WM
Li, SJ
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (07) : 1797 - 1820
[39] Morse index and symmetry for elliptic problems with nonlinear mixed boundary conditions
Damascelli, Lucio
Pacella, Filomena
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2019, 149 (02) : 305 - 324
[40] Nontrivial solutions for a nonlinear discrete elliptic equation with periodic boundary conditions
Bai, Liang
Zhang, Guang
APPLIED MATHEMATICS AND COMPUTATION, 2009, 210 (02) : 321 - 333

← 1 2 3 4 5 →