The Schauder Theorem and Applications

2013 ◽  
pp. 83-107
Author(s):  
Pablo Amster
Keyword(s):  
Schauder Theorem

scholarly journals On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Dongming Nie ◽  
Azmat Ullah Khan Niazi ◽  
Bilal Ahmed
Keyword(s):  
Differential Equations ◽  
Existence Of A Solution ◽  
Neutral Differential Equations ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Functional Differential ◽  
Schauder Theorem ◽  
Equations With Delay ◽  
Rassias Stability ◽  
Fractional Functional

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.

A quantitative Schauder Theorem

1984 ◽  
Vol 185 (2) ◽  
pp. 243-245 ◽  
Author(s):  
Robin Harte
Keyword(s):  
Schauder Theorem

Quasi-compactness of linear operators on Banach spaces: New properties and application to Markov chains

2020 ◽  
pp. 2150060
Author(s):  
Leila Mebarki ◽  
Bekkai Messirdi ◽  
Mohammed Benharrat
Keyword(s):  
Banach Space ◽  
Markov Chains ◽  
Banach Spaces ◽  
Invariant Subspaces ◽  
Linear Operators ◽  
Fredholm Alternative ◽  
Riesz Operators ◽  
Algebraic Operations ◽  
Mathematical Literature ◽  
Schauder Theorem

The purpose of this paper is to study the notion of quasi-compact linear operators acting in a Banach space. This class of operators contains the set of compact, polynomially compact, quasi-nilpotent and that of all Riesz operators. We show the equivalence between different definitions of quasi-compactness known in the mathematical literature and we present several general theorems about quasi-compact endomorphisms: stability under algebraic operations, extension of Schauder theorem and the Fredholm alternative. We also study the question of existence of invariant subspaces and we examine the class of semigroups for quasi-compact operators. The obtained results are used to describe Markov chains.

A Leray-Schauder theorem for a class of nonlinear operators

1969 ◽  
Vol 182 (3) ◽  
pp. 207-212 ◽  
Author(s):  
D. E. Edmunds ◽  
J. R. L. Webb
Keyword(s):  
Nonlinear Operators ◽  
Schauder Theorem

Analogs of the Schauder theorem that use anticompacta

2016 ◽  
Vol 99 (5-6) ◽  
pp. 954-958 ◽  
Author(s):  
F. S. Stonyakin
Keyword(s):  
Schauder Theorem
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