## Structure and dimension of global branches of solutions to multiparameter nonlinear equations

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- by J. Ize, I. Massabò, J. Pejsachowicz and A. Vignoli PDF
- Trans. Amer. Math. Soc.
**291**(1985), 383-435 Request permission

## Abstract:

This paper is concerned with the topological dimension of global branches of solutions appearing in different problems of Nonlinear Analysis, in particular multiparameter (including infinite dimensional) continuation and bifurcation problems. By considering an extension of the notion of essential maps defined on sets and using elementary point set topology, we are able to unify and extend, in a selfcontained fashion, most of the recent results on such problems. Our theory applies whenever any generalized degree theory with the boundary dependence property may be used, but with no need of algebraic structures. Our applications to continuation and bifurcation follow from the nontriviality of a local invariant, in the stable homotopy group of a sphere, and give information on the local dimension and behavior of the sets of solutions, of bifurcation points and of continuation points.## References

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## Additional Information

- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**291**(1985), 383-435 - MSC: Primary 58E07; Secondary 47H15
- DOI: https://doi.org/10.1090/S0002-9947-1985-0800246-0
- MathSciNet review: 800246