scholarly journals Topological degree method for the rotationally symmetric $L_p$-Minkowski problem

2015 ◽  
Vol 36 (2) ◽  
pp. 971-980 ◽  
Author(s):  
Jian Lu ◽  
Huaiyu Jian
Keyword(s):  
Topological Degree ◽  
Minkowski Problem ◽  
Rotationally Symmetric ◽  
Topological Degree Method

scholarly journals Application of topological degree method in quantitative behavior of fractional differential equations

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 421-432
Author(s):  
Rahman ur ◽  
Saeed Ahmad ◽  
Fazal Haq
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Research Article ◽  
Fractional Differential ◽  
Topological Degree Method

In the present manuscript we incorporate fractional order Caputo derivative to study a class of non-integer order differential equation. For existence and uniqueness of solution some results from fixed point theory is on our disposal. The method used for exploring these existence results is topological degree method and some auxiliary conditions are developed for stability analysis. For further elaboration an illustrative example is provided in the last part of the research article.

scholarly journals Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent

2021 ◽  
Vol 7 (1) ◽  
pp. 50-65
Author(s):  
Mustapha Ait Hammou ◽  
Elhoussine Azroul
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Problem ◽  
Topological Degree ◽  
Variable Exponent ◽  
Existence Of Solutions ◽  
Nonlinear Elliptic Problem ◽  
Technical Approach ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Topological Degree Method

AbstractThe aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form\left\{ {\matrix{{A\left( u \right) = f} \hfill & {in} \hfill & \Omega \hfill \cr {u = 0} \hfill & {on} \hfill & {\partial \Omega } \hfill \cr } } \right.where A(u) = −diva(x, u, ∇u) is a Leray-Lions operator and f ∈ W−1,p′(.)(Ω) with p(x) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.

scholarly journals Generalized Solutions for Nonlocal Elliptic Equations and Systems with Nonlinear Singularities

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Youtao Wang ◽  
Guangcun Lu
Keyword(s):  
Elliptic Equations ◽  
Topological Degree ◽  
Existence Of Solutions ◽  
Generalized Solutions ◽  
Singular Nonlinearity ◽  
Topological Degree Method

We use the topological degree method to study the existence of solutions for nonlocal elliptic equations (systems) with a strong singular nonlinearity.

scholarly journals Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shiqi Ma ◽  
Xuemei Zhang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Topological Degree ◽  
Boundary Value ◽  
Nonlocal Problem ◽  
Second Order ◽  
Technical Level ◽  
Point Boundary ◽  
Nonlocal Problems ◽  
Topological Degree Method

Abstract In this paper we consider sharp conditions on ω and f for the existence of $C^{1}[0,1]$ C 1 [ 0 , 1 ] positive solutions to a second-order singular nonlocal problem $u''(t)+\omega (t)f(t,u(t))=0$ u ″ ( t ) + ω ( t ) f ( t , u ( t ) ) = 0 , $u(0)=u(1)=\int _{0} ^{1}g(t)u(t)\,dt$ u ( 0 ) = u ( 1 ) = ∫ 0 1 g ( t ) u ( t ) d t ; it turns out that this case is more difficult to handle than two point boundary value problems and needs some new ingredients in the arguments. On the technical level, we adopt the topological degree method.

scholarly journals Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Usman Riaz ◽  
Akbar Zada
Keyword(s):  
Topological Degree ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Topological Degree Method

AbstractThis article is devoted to establish the existence of solution of $\left(\alpha ,\beta \right)$-order coupled implicit fractional differential equation with initial conditions, using Laplace transform method. The topological degree theory is used to obtain sufficient conditions for uniqueness and at least one solution of the considered system. Beside this, Ulam’s type stabilities are discussed for the proposed system. To support our main results, we present an example.

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