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A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms

Shabani Rokn E Vafa, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.na.2017.02.010
  3. Abstract:
  4. We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−c, where a,c,m and d are positive constants, Ω a bounded smooth domain in RN, and b(x) is a nonnegative function on Ω¯, with Ω0 a region such that Ω¯0⊂Ω and Ω¯0={x∈Ω:b(x)=0}. Under the strong growth rate assumption, that is, when a is greater than the first eigenvalue of −Δ in Ω0 with Dirichlet boundary condition, we show that the equation has at least one positive solution for 0≤d0. In addition, in case c
  5. Keywords:
  6. Strong growth rate ; Mountain pass theorem ; Boundary conditions ; Dirichlet boundary condition ; Existence and multiplicities ; Logistic equations ; Diffusive logistic equation ; Multiplicity results ; Nonnegative functions ; Positive constant ; Strong growth ; Eigenvalues and eigenfunctions
  7. Source: Nonlinear Analysis, Theory, Methods and Applications ; Volume 156 , 2017 , Pages 1-16 ; 0362546X (ISSN)
  8. URL: https://www.sciencedirect.com/science/article/pii/S0362546X17300469