Diffusive logistic equation with constant yield harvesting, I: Steady States

Authors:
Shobha Oruganti, Junping Shi and Ratnasingham Shivaji

Journal:
Trans. Amer. Math. Soc. **354** (2002), 3601-3619

MSC (2000):
Primary 35J65; Secondary 35J25, 35B32, 92D25

DOI:
https://doi.org/10.1090/S0002-9947-02-03005-2

Published electronically:
May 7, 2002

MathSciNet review:
1911513

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Abstract: We consider a reaction-diffusion equation which models the constant yield harvesting to a spatially heterogeneous population which satisfies a logistic growth. We prove the existence, uniqueness and stability of the maximal steady state solutions under certain conditions, and we also classify all steady state solutions under more restricted conditions. Exact global bifurcation diagrams are obtained in the latter case. Our method is a combination of comparison arguments and bifurcation theory.

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Additional Information

**Shobha Oruganti**

Affiliation:
Department of Mathematics, Mississippi State University, Mississippi State, Mississippi 39762

Email:
so1@ra.msstate.edu

**Junping Shi**

Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187 and Department of Mathematics, Harbin Normal University, Harbin, Heilongjiang, P. R. China 150080

Email:
shij@math.wm.edu

**Ratnasingham Shivaji**

Affiliation:
Department of Mathematics, Mississippi State University, Mississippi State, Mississippi 39762

Email:
shivaji@ra.msstate.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-03005-2

Keywords:
Diffusive logistic equation,
harvesting,
steady states,
comparison methods,
bifurcation

Received by editor(s):
September 5, 2001

Received by editor(s) in revised form:
October 15, 2001

Published electronically:
May 7, 2002

Article copyright:
© Copyright 2002
American Mathematical Society