The Topological Degree

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.

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Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-021-00618-7 ◽

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.

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

Advances in Difference Equations ◽

10.1186/s13662-020-02986-2 ◽

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.

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A note on topological degree theory for holomorphic maps

Israel Journal of Mathematics ◽

10.1007/bf02761969 ◽

1973 ◽

Vol 16 (1) ◽

pp. 46-52 ◽

Cited By ~ 4

Author(s):

Paul H. Rabinowitz

Keyword(s):

Topological Degree ◽

Degree Theory ◽

Holomorphic Maps ◽

Topological Degree Theory

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An Optimal Complexity Algorithm for Computing the Topological Degree in Two Dimensions

SIAM Journal on Scientific and Statistical Computing ◽

10.1137/0910042 ◽

1989 ◽

Vol 10 (4) ◽

pp. 686-698 ◽

Cited By ~ 8

Author(s):

T. Boult ◽

K. Sikorski

Keyword(s):

Topological Degree ◽

Two Dimensions ◽

Optimal Complexity ◽

Complexity Algorithm

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

Communications in Contemporary Mathematics ◽

10.1142/s0219199721500735 ◽

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.

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AN APPLICATION OF THE TOPOLOGICAL DEGREE TO GRAVITATIONAL LENSES

Modern Physics Letters A ◽

10.1142/s0217732398000115 ◽

1998 ◽

Vol 13 (02) ◽

pp. 83-86 ◽

Cited By ~ 4

Author(s):

MARCO LOMBARDI

Keyword(s):

Point Source ◽

Mass Distribution ◽

Topological Degree ◽

General Theorem ◽

Gravitational Lens ◽

Gravitational Lenses ◽

General Proof ◽

Special Case

In this letter we provide a new proof of a general theorem on gravitational lenses, first proven by Burke (1981) for the special case of thin lenses. The theorem states that a transparent gravitational lens with non-singular mass distribution produces an odd number of images of a point source. Our general proof shows that the topological degree finds natural and interesting applications in the theory of gravitational lenses.

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