A short note on a simple proof of Schauder's fixed point theorem and its generalization without continuity and compactness assumptions

2016 ◽  
Vol 10 ◽  
pp. 933-938 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Simple Proof ◽  
Short Note ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem

scholarly journals A Periodic Solution of the Generalized Forced Liénard Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Zahra Goodarzi ◽  
Abdolrahman Razani
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Liénard Equation ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Lienard Equation

We consider the generalized forced Liénard equation as follows:(ϕp(x′))′+(f(x)+k(x)x′)x′+g(x)=p(t)+s. By applying Schauder's fixed point theorem, the existence of at least one periodic solution of this equation is proved.

scholarly journals Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xinguang Zhang ◽  
Cuiling Mao ◽  
Yonghong Wu ◽  
Hua Su
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Differential System ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Two Parameters

We establish the existence of positive solutions to a class of singular nonlocal fractional order differential system depending on two parameters. Our methods are based on Schauder’s fixed point theorem.

ASYMPTOTIC EXPANSION FOR DIFFERENCE EQUATIONS WITH INFINITE DELAY

2009 ◽  
Vol 02 (01) ◽  
pp. 19-40
Author(s):  
Claudio Cuevas ◽  
Luis del Campo
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Asymptotic Expansion ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Infinite Delay ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Volterra Difference Equations

Using summable dichotomies and Schauder's fixed point theorem, we obtain existence, asymptotic behavior and compactness properties, of convergent solutions for difference equations with infinite delay. Applications on Volterra difference equations with infinite delay are shown.

scholarly journals The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order1< α<2

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xianghu Liu ◽  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Schauder’S Fixed Point Theorem ◽  
Sufficient Condition ◽  
Optimal Controls ◽  
Schauder's Fixed Point Theorem ◽  
Gronwall’S Inequality ◽  
Impulsive Equations

We study the existence of solutions and optimal controls for some fractional impulsive equations of order1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results.

scholarly journals Existence and Attractivity Results for Coupled Systems of Nonlinear Volterra–Stieltjes Multidelay Fractional Partial Integral Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Naima Hamidi ◽  
Gaston N’Guérékata
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Schauder’S Fixed Point Theorem ◽  
Integral System ◽  
Schauder's Fixed Point Theorem ◽  
Globally Attractive

We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive.

Sign in / Sign up

Export Citation Format

Share Document