Loading...

Diffusive logistic equations with harvesting and heterogeneity under strong growth rate

Shabani Rokn-E-Vafa, S ; Sharif University of Technology | 2019

158 Viewed
  1. Type of Document: Article
  2. DOI: 10.1515/anona-2016-0208
  3. Publisher: De Gruyter , 2019
  4. Abstract:
  5. We consider the equation (equation presented) where Ω is a smooth bounded domain in ℝ N , b(x) and h(x) are nonnegative functions, and there exists Ω 0 ⊃ Ω such that {x : b(x) = 0} = Ω0. We investigate the existence of positive solutions of this equation for c large under the strong growth rate assumption a ≥ λ 1 (Ω0), where λ 1 (Ω0) is the first eigenvalue of the δ in Ω0 with Dirichlet boundary condition. We show that if h = 0 in Ω\u03a90, then our equation has a unique positive solution for all c large, provided that a is in a right neighborhood of λ 1 (Ω0). For this purpose, we prove and utilize some new results on the positive solution set of this equation in the weak growth rate case
  6. Keywords:
  7. Comparison principles ; Harvesting ; Heterogeneity ; Logistic equation ; Stable solutions ; Strong growth rate
  8. Source: Advances in Nonlinear Analysis ; Volume 8, Issue 1 , 2019 , Pages 455-467 ; 21919496 (ISSN)
  9. URL: https://www.degruyter.com/view/journals/anona/8/1/article-p455.xml?language=en