Bifurcation and stability results for an equation arising in population genetics

K. J. Brown; Song-Sun Lin

doi:10.1007/BF01789483

Bifurcation and stability results for an equation arising in population genetics

K. J. Brown, Song-Sun Lin

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider a semilinear elliptic boundary value problem, which arises in population genetics. Although there is no obvious corresponding linearized problem, we establish, by using Implicit Function Theorem methods, necessary and sufficient conditions for bifurcation to occur from a branch of trivial solutions. The stability of the bifurcating solutions is also investigated.

Original language	English
Pages (from-to)	375-387
Number of pages	13
Journal	Annali di Matematica Pura ed Applicata
Volume	128
Issue number	1
DOIs	https://doi.org/10.1007/BF01789483
State	Published - 1 Dec 1981

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abstract = "We consider a semilinear elliptic boundary value problem, which arises in population genetics. Although there is no obvious corresponding linearized problem, we establish, by using Implicit Function Theorem methods, necessary and sufficient conditions for bifurcation to occur from a branch of trivial solutions. The stability of the bifurcating solutions is also investigated.",

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AU - Lin, Song-Sun

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N2 - We consider a semilinear elliptic boundary value problem, which arises in population genetics. Although there is no obvious corresponding linearized problem, we establish, by using Implicit Function Theorem methods, necessary and sufficient conditions for bifurcation to occur from a branch of trivial solutions. The stability of the bifurcating solutions is also investigated.

AB - We consider a semilinear elliptic boundary value problem, which arises in population genetics. Although there is no obvious corresponding linearized problem, we establish, by using Implicit Function Theorem methods, necessary and sufficient conditions for bifurcation to occur from a branch of trivial solutions. The stability of the bifurcating solutions is also investigated.

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M3 - Article

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JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

SN - 0373-3114

IS - 1

ER -

Bifurcation and stability results for an equation arising in population genetics

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