Opuscula Mathematica

Opuscula Math.
 28
, no. 4
 (), 541-560
Opuscula Mathematica

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


Abstract. 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.
Keywords: Brouwer degree, nonlinear difference equations.
Mathematics Subject Classification: 47H14, 47J25, 34G20.
Cite this article as:
Jean Mawhin, Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations, Opuscula Math. 28, no. 4 (2008), 541-560
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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