a1 Departamento de Ecuaciones Funcionales, Universidad Complutense de Madrid, 28040-Madrid, Spain.
Let us consider the abstract equation
(0.1) L () u + F (,u) = 0,
where F (,u) = 0 (|u|2) for near zero. In this paper we define a multiplicity depending only on L () allowing us to obtain the following result: “Odd multiplicity entails bifurcation and, if the multiplicity is even, it is possible to find F (,u) such that the only solution to (0.1) near the origin are the trivial ones”.
(Received July 08 1986)