Topological degree of pseudopositive mappings
type: Item
instance of: scholarly article
title: Topological degree of pseudopositive mappings
zbMATH Open document ID: 0596.47051
published in: Acta Mathematica Vietnamica
publication date: 1984-01-01T00:00:00Z
review text: Let E and F be two real separable Banach spaces, and D be a nonvoid open subset of E. Let \(f: \bar D\to F\) be proper and continuous on the closure \(\bar D\) of D and twice continuously differentiable on D. Then f is said to be pseudopositive on \(\bar D\) if \(f'(x)\) is a Fredholm operator of index 0 and the dimension of the kernel of \(f'(x)\) is even for every x in D. Using the technique of \textit{M. W. Hirsch} [Proc. Am. Math. Soc. 14, 364-365 (1963; Zbl 0113.167)], we established a definition of topological degree for the pseudopositive mappings. The values of this topological degree are positive integers and might be used to estimate the numbers of solutions of equations involved by the pseudopositive mappings.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 3960371
zbMATH Keywords: proper analytic Fredholm mapping of index zero
zbMATH Keywords: Fredholm operator of index
zbMATH Keywords: topological degree for the pseudopositive mappings
author: Duong Minh Duc
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3960371