THE PERIODIC-PARABOLIC LOGISTIC EQUATION ON RN

被引:17
作者
Peng, Rui [1 ,2 ]
Wei, Dong [3 ]
机构
[1] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Peoples R China
[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
[3] Hebei Univ Engn, Handan City 056038, Hebei Province, Peoples R China
关键词
Periodic-parabolic logistic equation; entire space; positive periodic solution; uniqueness; asymptotic behavior; SEMILINEAR ELLIPTIC-EQUATIONS; BOUNDARY BLOW-UP; POSITIVE SOLUTIONS; INDEFINITE; UNIQUENESS; EXISTENCE; BEHAVIOR; GROWTH;
D O I
10.3934/dcds.2012.32.619
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we investigate the periodic-parabolic logistic equation on the entire space R-N (N >= 1): {partial derivative(t)u - Delta u = a(x, t)u - b(x, t)u(p) in R-N x (0, T), u(x, 0) = u(x, T) in R-N, where the constants T > 0 and p > 1, and the functions a, b with b > 0 are smooth in R-N x R and T-periodic in time. Under the assumptions that a(x, t)/vertical bar x vertical bar(gamma) and b(x, t)/vertical bar x vertical bar(tau) are bounded away from 0 and infinity for all large vertical bar x vertical bar, where the constants gamma > -2 and tau is an element of R, we study the existence and uniqueness of positive T-periodic solutions. In particular, we determine the asymptotic behavior of the unique positive T-periodic solution as vertical bar x vertical bar -> infinity, which turns out to depend on the sign of gamma. Our investigation considerably generalizes the existing results.
引用
收藏
页码:619 / 641
页数:23
相关论文
共 50 条
  • [31] The periodic principal eigenvalues with applications to the nonlocal dispersal logistic equation
    Sun, Jian-Wen
    Li, Wan-Tong
    Wang, Zhi-Cheng
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (02) : 934 - 971
  • [32] On a degenerate parabolic equation with singular convection
    Li, SH
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (01) : 175 - 197
  • [33] A singular parabolic equation: Existence, stabilization
    Badra, Mehdi
    Bal, Kaushik
    Giacomoni, Jacques
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (09) : 5042 - 5075
  • [34] Periodic parabolic equation involving singular nonlinearity with variable exponent
    Charkaoui, Abderrahim
    Taourirte, Laila
    Alaa, Nour Eddine
    [J]. RICERCHE DI MATEMATICA, 2023, 72 (02) : 973 - 989
  • [35] Parabolic logistic equation with harvesting involving the fractional Laplacian
    Chhetri, Maya
    Girg, Petr
    Hollifield, Elliott
    Kotrla, Lukas
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (06):
  • [36] On an Anisotropic Logistic Equation
    Gasinski, Leszek
    Papageorgiou, Nikolaos S.
    [J]. MATHEMATICS, 2024, 12 (09)
  • [37] Periodic solutions of a class of degenerate parabolic system with delays
    Wang, Yifu
    Yin, Jingxue
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 380 (01) : 57 - 68
  • [38] On a degenerate nonlocal parabolic equation with variable source
    Sert, Ugur
    Shmarev, Sergey
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 484 (01)
  • [39] Study of Solutions to a Fourth Order Parabolic Equation
    Liang, Bo
    Peng, Xiting
    Shen, Huiying
    [J]. MATHEMATICAL MODELLING AND ANALYSIS, 2016, 21 (01) : 1 - 15
  • [40] Time Periodic Solutions for a Pseudo-parabolic Type Equation with Weakly Nonlinear Periodic Sources
    Yinghua Li
    Yang Cao
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38 : 667 - 682