Branching and bifurcation

Patrick M. Fitzpatrick; Jacobo Pejsachowicz

doi:10.3934/dcdss.2019127

Article Contents

2019, Volume 12, Issue 7: 1955-1975. Doi: 10.3934/dcdss.2019127

This issue Previous Article Least energy solutions for fractional Kirchhoff type equations involving critical growth Next Article Multiple solutions for a critical quasilinear equation with Hardy potential

Branching and bifurcation

Patrick M. Fitzpatrick^1, and
Jacobo Pejsachowicz^2, ,

1.
Department of Mathematics, University of Maryland, 4176 Campus Dr, College Park, MD 20742, USA
2.
INDAM, Dipartimento di Scienze Matematiche, Politecnico di Torino, Duca degli Abruzzi 24, 10129 Torino, Italy

^* Corresponding author
^* Corresponding author

Received: December 31, 2017

Revised: July 31, 2018

Published: June 2019

J. Pejsachowicz is supported by GNAMPA-INDAM

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Abstract

By relating the set of branch points $ \mathcal{B} (f) $ of a Fredholm mapping $ f $ to linearized bifurcation, we show, among other things, that under mild local assumptions at a single point, the set $ \mathcal B(f) $ is sufficiently large to separate the domain of the mapping. In the variational case, we will also provide estimates from below for the number of connected components of the complement of $ \mathcal B(f). $

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Mathematics Subject Classification: Primary: 58E07; Secondary: 47J15, 37J45, 37J20.

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