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Global Bifurcations of Solutions of Elliptic Differential Equations

✍ Scribed by Sławomir Rybicki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
159 KB
Volume
217
Category
Article
ISSN
0022-247X

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✦ Synopsis

The aim of this article is to prove global bifurcation theorems for S 1 -equivariant potential operators of the form ''compact perturbation of identity.'' As an application we prove that components of the set of nontrivial solutions of system

which bifurcate from the set of trivial solutions are unbounded in suitably chosen space. The important point to note here is that our results apply only to systems with an even number of equations. As the main tool we use degree theory for 1 w x S -equivariant potential operators constructed by the author in 16 and developed w x in 17 .

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