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Optimal results in local bifurcation theory

Published online by Cambridge University Press:  17 April 2009

J. Esquinas  and
J. López-Gómez
J. Esquinas
Affiliation:
Departamento de Ecuaciones Funcionales, Universidad Complutense de Madrid, 28040-Madrid, Spain.
J. López-Gómez
Affiliation:
Departamento de Ecuaciones Funcionales, Universidad Complutense de Madrid, 28040-Madrid, Spain.
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Abstract

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Let us consider the abstract equation

(0.1) L (ɛ) u + F (ɛ,u) = 0,

where F (ɛ,u) = 0 (|u|2) for ɛ near zero. In this paper we define a multiplicity depending only on L (ɛ) allowing us to obtain the following result: “Odd multiplicity entails bifurcation and, if the multiplicity is even, it is possible to find F (ɛ,u) such that the only solution to (0.1) near the origin are the trivial ones”.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 25 - 37
Copyright
Copyright © Australian Mathematical Society 1987

References

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