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Counting solutions in bifurcation problems

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Abstract

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 one means a component that is bounded in one direction of the parameter. The spectrum of linearization of the equation at the trivial state is not assumed to be discrete.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain

    J. López-Gómez & C. Mora-Corral

Authors
  1. J. López-Gómez
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  2. C. Mora-Corral
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Corresponding author

Correspondence to J. López-Gómez.

Additional information

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 149–167, 2006.

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López-Gómez, J., Mora-Corral, C. Counting solutions in bifurcation problems. J Math Sci 150, 2395–2407 (2008). https://doi.org/10.1007/s10958-008-0138-5

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  • DOI: https://doi.org/10.1007/s10958-008-0138-5

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