TY  - JOUR
ID  - Mawhin2008
LB  - Mawhin2008
AU  - Mawhin, Jean
TI  - Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations
ST  - Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 4
SP  - 541
EP  - 560
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.4.541
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.4.541
AB  - The aim of this note is to describe the continuation theorem of [J. Mawhin, Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces, J. Differential Equations 12 (1972), 610–636, J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Reg. Conf. in Math., No 40, American Math. Soc., Providence, RI, 1979] 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 [J. Leray, J. Schauder, Topologie et équations fonctionnelles, Ann. Scient. Ecole Normale Sup. (3) 51 (1934), 45–78], which is fundamental for their construction of Leray-Schauder's degree in normed vector spaces.
KW  - Brouwer degree
KW  - nonlinear difference equations
SN  - 1232-9274
ER  -