scholarly journals A Problem Concerning Yamabe-Type Operators of Negative Admissible Metrics

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jin Liang ◽  
Huan Zhu
Keyword(s):  
Functional Analysis ◽  
Maximum Principle ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Degree Theory ◽  
Yamabe Problem ◽  
Existence And Uniqueness Theorem ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
The Maximum Principle

This paper is about a problem concerning nonlinear Yamabe-type operators of negative admissible metrics. We first give a result onσkYamabe problem of negative admissible metrics by virtue of the degree theory in nonlinear functional analysis and the maximum principle and then establish an existence and uniqueness theorem for the solutions to the problem.

scholarly journals Applications of the Bielecki renorming technique

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Mihály Bessenyei ◽  
Zsolt Páles
Keyword(s):  
Functional Analysis ◽  
Global Existence ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Existence And Uniqueness Theorem ◽  
Banach Contraction ◽  
Global Existence And Uniqueness ◽  
The Banach Contraction Principle ◽  
Elegant Proof

AbstractThe renorming technique allows one to apply the Banach Contraction Principle for maps which are not contractions with respect to the original metric. This method was invented by Bielecki and manifested in an extremely elegant proof of the Global Existence and Uniqueness Theorem for ODEs. The present paper provides further extensions and applications of Bielecki’s method to problems stemming from functional analysis and from the theory of functional equations.

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

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