Perturbation effects in nonlinear eigenvalue problems

被引：6
|
作者：
Radulescu, Vicentiu [1 ,2 ]
Repovs, Dusan [3 ,4 ]
机构：
[1] Acad Romana, Inst Math Simion Stoilow, Bucharest, Romania
[2] Univ Craiova, Dept Math, Craiova 200585, Romania
[3] Univ Ljubljana, Fac Math & Phys, Ljubljana 1001, Slovenia
[4] Univ Ljubljana, Fac Educ, Ljubljana 1001, Slovenia
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 08期
关键词：
Logistic equation; Nonlinear eigenvalue problem; Positive entire solution; Spectrum; Anisotropic potential; Perturbation; Population dynamics; EQUATIONS;
D O I：
10.1016/j.na.2008.12.036
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish the complete bifurcation diagram for a class of nonlinear problems on the whole space. Our model corresponds to a class of semilinear elliptic equations with logistic type nonlinearity and absorption. Since this problem arises in population dynamics or in fishery or hunting management, we are interested only in situations allowing the existence of positive solutions. The proofs combine elliptic estimates with the method of sub- and super-solutions. (c) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3030 / 3038
页数：9
相关论文
共 50 条
  • [1] NLEVP: A Collection of Nonlinear Eigenvalue Problems
    Betcke, Timo
    Higham, Nicholas J.
    Mehrmann, Volker
    Schroeder, Christian
    Tisseur, Francoise
    ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2013, 39 (02):
  • [2] PERTURBATION ANALYSIS FOR PALINDROMIC AND ANTI-PALINDROMIC NONLINEAR EIGENVALUE PROBLEMS
    Ahmad, Sk Safique
    ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2019, 51 : 151 - 168
  • [3] ASYMPTOTIC PERTURBATION OF PALINDROMIC EIGENVALUE PROBLEMS
    Li, Tie-Xiang
    Chu, Eric King-wah
    Wang, Chern-Shuh
    TAIWANESE JOURNAL OF MATHEMATICS, 2010, 14 (3A): : 781 - 793
  • [4] Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems
    Yuji Nakatsukasa
    BIT Numerical Mathematics, 2010, 50 : 109 - 121
  • [5] Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems
    Nakatsukasa, Yuji
    BIT NUMERICAL MATHEMATICS, 2010, 50 (01) : 109 - 121
  • [6] Perturbation theory of nonlinear, non-self-adjoint eigenvalue problems: Semisimple eigenvalues
    Orchini, Alessandro
    Mensah, Georg A.
    Moeck, Jonas P.
    JOURNAL OF SOUND AND VIBRATION, 2021, 507
  • [7] A full multigrid method for nonlinear eigenvalue problems
    Jia, ShangHui
    Xie, HeHu
    Xie, ManTing
    Xu, Fei
    SCIENCE CHINA-MATHEMATICS, 2016, 59 (10) : 2037 - 2048
  • [8] A Modified Newton Method for Nonlinear Eigenvalue Problems
    Chen, Xiao-Ping
    Dai, Hua
    EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2018, 8 (01) : 139 - 150
  • [9] Transition between nonlinear and linear eigenvalue problems
    Jiang, Guosheng
    Liu, Yongjie
    Liu, Zhaoli
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (12) : 10919 - 10936
  • [10] Nonlinear eigenvalue problems of the elastica
    Ram, Y. M.
    MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2014, 45 (02) : 408 - 423
12345