FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 149-167

J. López-Gómez

C. Mora-Corral

Abstract

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In this paper, we use the topological degree to obtain some sharp lower bounds for the number of solutions of the parameter slices of the semi-bounded components of the set of nontrivial solutions of an abstract nonlinear equation with a trivial state. By a semi-bounded component, we mean a component that is bounded in one direction of the parameter. The spectrum of the linearization of the equation at the trivial state is not assumed to be discrete.

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