Computing the topological degree of a mapping inR n

1975 ◽  
Vol 25 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Frank Stenger
Keyword(s):  
Topological Degree ◽  
Degree Of A Mapping

A reliable algorithm for computing the topological degree of a mapping in R2

2008 ◽  
Vol 196 (2) ◽  
pp. 666-678 ◽  
Author(s):  
K.H. Ko ◽  
T. Sakkalis ◽  
N.M. Patrikalakis
Keyword(s):  
Topological Degree ◽  
Degree Of A Mapping

scholarly journals On the homotopy property of degree for multivalued noncompact maps

1980 ◽  
Vol 21 (1) ◽  
pp. 125-130
Author(s):  
J. R. L. Webb
Keyword(s):  
Topological Degree ◽  
Contraction Mappings ◽  
Homotopy Property ◽  
Compact Perturbations ◽  
Degree Of A Mapping

Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].

scholarly journals An algorithm for the topological degree of a mapping in $n$-space

1975 ◽  
Vol 81 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Frank Stenger
Keyword(s):  
Topological Degree ◽  
Degree Of A Mapping

scholarly journals On the homotopy property of degree for multivalued noncompact maps

1980 ◽  
Vol 21 (2) ◽  
pp. 125-130 ◽  
Author(s):  
J. R. L. Webb
Keyword(s):  
Topological Degree ◽  
Contraction Mappings ◽  
Homotopy Property ◽  
Compact Perturbations ◽  
Degree Of A Mapping

Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].

Generalized Topological Degree and Semilinear Equations

1995 ◽  
Author(s):  
Wolodymyr V. Petryshyn
Keyword(s):  
Topological Degree ◽  
Semilinear Equations

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

A note on topological degree theory for holomorphic maps

1973 ◽  
Vol 16 (1) ◽  
pp. 46-52 ◽  
Author(s):  
Paul H. Rabinowitz
Keyword(s):  
Topological Degree ◽  
Degree Theory ◽  
Holomorphic Maps ◽  
Topological Degree Theory
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