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Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations

Mawhin J.

Opuscula Mathematica

2008

Vol. 28, no. 4

541-560

The aim of this note is to describe the continuation theorem of [39,40] directly in the context of Brouwer degree, providing in this way a simple frame for multiple applications to nonlinear difference equations, and to show how the corresponding reduction property can be seen as an extension of the well-known reduction formula of Leray and Schauder [24], which is fundamental for their construction of Leray-Schauder's degree in normed vector spaces.