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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 195, Issue 4, pp 1347–1371 | Cite as

Generalizing the Poincaré–Miranda theorem: the avoiding cones condition

  • Alessandro FondaEmail author
  • Paolo Gidoni
Article

Abstract

After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \(\pm \)1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

Keywords

Poincaré–Miranda Fixed point Topological degree 

Mathematics Subject Classification

47H10 54H25 37C25 

Notes

Acknowledgments

We thank the referee for suggesting us simpler proofs of Theorem 3 and Proposition 7. We also acknowledge the support of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dipartimento di Matematica e GeoscienzeUniversità di TriesteTriesteItaly
  2. 2.SISSA - International School for Advanced StudiesTriesteItaly

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