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Optimal results in local bifurcation theory
Published online by Cambridge University Press: 17 April 2009
Abstract
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”.
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- Copyright © Australian Mathematical Society 1987
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