On the topological degree of planar maps avoiding normal cones

2019 ◽  
pp. 1
Author(s):  
Alessandro Fonda ◽  
Giuliano Klun
Keyword(s):  
Topological Degree ◽  
Normal Cones ◽  
Planar Maps

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.

scholarly journals Normal cones to infinite intersections

2010 ◽  
Vol 72 (11) ◽  
pp. 3911-3917 ◽  
Author(s):  
Thomas I. Seidman
Keyword(s):  
Normal Cones

THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE

2009 ◽  
Vol 19 (01) ◽  
pp. 117-133 ◽  
Author(s):  
MATEJ MENCINGER ◽  
MILAN KUTNJAK
Keyword(s):  
Algebraic Approach ◽  
Dynamical Analysis ◽  
Algebraic Classification ◽  
Commutative Algebras ◽  
Planar Maps ◽  
Points Of View ◽  
One To One

The dynamics of discrete homogeneous quadratic planar maps is considered via the algebraic approach. There is a one-to-one correspondence between these systems and 2D commutative algebras (c.f. [Markus, 1960]). In particular, we consider the systems corresponding to algebras which contain some nilpotents of rank two (i.e. NQ-systems). Markus algebraic classification is used to obtain the class representatives. The case-by-case dynamical analysis is presented. It is proven that there is no chaos in NQ-systems. Yet, some cases are really interesting from the dynamical and bifurcational points of view.

Estimates of the topological degree of a class of piecewise linear maps with applications

2021 ◽  
pp. 2150073
Author(s):  
Laura Poggiolini ◽  
Marco Spadini
Keyword(s):  
Topological Degree ◽  
Piecewise Linear ◽  
Nonlinear Problems ◽  
Text Structure ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Classical Integral ◽  
Computation Formula

We provide some new estimates for the topological degree of a class of continuous and piecewise linear maps based on a classical integral computation formula. We provide applications to some nonlinear problems that exhibit a local [Formula: see text] structure.

The Design and Implementation of Planar Maps in CGAL

1999 ◽  
pp. 154-168 ◽  
Author(s):  
Eyal Flato ◽  
Dan Halperin ◽  
Iddo Hanniel ◽  
Oren Nechushtan
Keyword(s):  
Design And Implementation ◽  
Planar Maps
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