Counting solutions of nonlinear abstract equations
Keywords
Bifurcation theory, counting the number of solutions, fine topological structureAbstract
In this paper we use the topological degree to estimate the minimal number of solutions of the sections (defined by fixing a parameter) of the semi-bounded components of a general class of one-parameter abstract nonlinear equations by means of the {\it signature} of the semi-bounded component. A semi-bounded component is, roughly speaking, a component that is bounded along one direction of the parameter. The signature consists of the set of bifurcation values from the trivial state of the component together with their associated parity indices. The parity is a local invariant measuring the change of the local index of the trivial state.Downloads
Published
2004-12-01
How to Cite
1.
LÓPEZ-GÓMEZ, Julian and MORA-CORRAL, Carlos. Counting solutions of nonlinear abstract equations. Topological Methods in Nonlinear Analysis. Online. 1 December 2004. Vol. 24, no. 2, pp. 307 - 335. [Accessed 24 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0