Bulletin of the Australian Mathematical Society

Table of Contents - 1987 - Volume 36, Issue 01  

Research Article

Optimal results in local bifurcation theory

J. Esquinasa1 and J. López-Gómeza1

a1 Departamento de Ecuaciones Funcionales, Universidad Complutense de Madrid, 28040-Madrid, Spain.

Abstract

Let us consider the abstract equation

(0.1) L (xs025B) u + F (xs025B,u) = 0,

where F (xs025B,u) = 0 (|u|2) for xs025B near zero. In this paper we define a multiplicity depending only on L (xs025B) allowing us to obtain the following result: “Odd multiplicity entails bifurcation and, if the multiplicity is even, it is possible to find F (xs025B,u) such that the only solution to (0.1) near the origin are the trivial ones”.

(Received July 08 1986)