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New exact multiplicity results with an application to a population model

Author： Korman Philip Shi Junping

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.131, Iss.5, 2001-10, pp. : 1167-1182

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

We obtain some new exact multiplicity results for the Dirichlet boundary-value problemΔu + λf(u) = 0 for x ∈ Bⁿ, u = 0 for x ∈ ∂Bⁿon 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.

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