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

Author(s): Shobha Oruganti; Junping Shi; Ratnasingham Shivaji
Journal: Trans. Amer. Math. Soc. 354 (2002), 3601-3619.
MSC (2000): Primary 35J65; Secondary 35J25, 35B32, 92D25
Posted: May 7, 2002
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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: 10.1090/S0002-9947-02-03005-2
PII: S 0002-9947(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
Posted: May 7, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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