An application of Schauder’s fixed point theorem to the existence of solutions of impulsively differential equations

1995 ◽  
Vol 16 (4) ◽  
pp. 377-381
Author(s):  
Dong Yu-jun ◽  
Zou Er-xin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem

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.

scholarly journals Existence of Solutions for a Quasilinear System with Gradient Terms

2021 ◽  
pp. 239-246
Author(s):  
Leandro S. Tavares
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Growth Conditions ◽  
Quasilinear System ◽  
Schauder’S Fixed Point Theorem ◽  
Laplacian Operator ◽  
Schauder's Fixed Point Theorem

In this paper, it is considered the existence of solutions for a quasilinear system involving the p-Laplacian operator and gradient terms. The approach is based on sub-supersolution arguments and the Schauder's Fixed Point Theorem. The results in this paper allow to consider several growth conditions in the gradient and complete some recent contributions.

scholarly journals Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zhongwei Cao ◽  
Chengjun Yuan ◽  
Xiuling Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Singular Differential Equations ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Periodic Solutions ◽  
Weak Singularities

We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help.

scholarly journals Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

2021 ◽  
Vol 5 (4) ◽  
pp. 200
Author(s):  
Fatemeh Mottaghi ◽  
Chenkuan Li ◽  
Thabet Abdeljawad ◽  
Reza Saadati ◽  
Mohammad Bagher Ghaemi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Biological Systems ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems.

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

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