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New exact multiplicity results with an application to a population model

Published online by Cambridge University Press:  12 July 2007

Philip Korman  and
Junping Shi
Philip Korman
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
Junping Shi
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
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Abstract

We obtain some new exact multiplicity results for the Dirichlet boundary-value problem on a unit ball Bn in Rn. We consider several classes of nonlinearities f(u), including both positive and sign-changing cases. A crucial part of the proof is to establish positivity of solutions for the corresponding linearized problem. As an application we obtain exact multiplicity results for the Holling-Tanner population model.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1167 - 1182
Copyright
Copyright © Royal Society of Edinburgh 2001

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