Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Coexistence theorems of steady states for predator-prey interacting systems
HTML articles powered by AMS MathViewer

by Lige Li PDF
Trans. Amer. Math. Soc. 305 (1988), 143-166 Request permission

Abstract:

In this paper we give necessary and sufficient conditions for the existence of positive solutions of steady states for predator-prey systems under Dirichlet boundary conditions on $\Omega \Subset {{\mathbf {R}}^n}$. We show that the positive coexistence of predatorprey densities is completely determined by the "marginal density," the unique density of prey or predator while the other one is absent, i.e. the $({u_0}, 0)$ or $(0, {\nu _0})$. More specifically, the situation of coexistence is determined by the spectral behavior of certain operators related to these marginal densities and is also completely determined by the stability properties of these marginal densities. The main results are Theorems 1 and 4.2.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 35J60, 92A15
  • Retrieve articles in all journals with MSC: 35J60, 92A15
Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 143-166
  • MSC: Primary 35J60; Secondary 92A15
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0920151-1
  • MathSciNet review: 920151