scholarly journals Existence of solutions of first-order differential equations via a fixed point theorem for discontinuous operators

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Rubén Figueroa Sestelo ◽  
Rodrigo López Pouso
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
First Order ◽  
First Order Differential Equations

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 Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay

2017 ◽  
Author(s):  
Kazem Nouri ◽  
Marjan Nazari ◽  
Bagher Keramati
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Equations

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

scholarly journals EXISTENCE OF SOLUTIONS FOR IMPULSIVE NEUTRAL FUNCTIONAL INTEGRO DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

2017 ◽  
Vol 4 (3) ◽  
pp. 1-6
Author(s):  
Valliammal N ◽  
Ravichandran C
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Mild Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Integrodifferential Equations ◽  
Fractional Power Of Operators

In this paper, by using fractional power of operators and Sadovskii’s fixed point theorem, we study the existence of mild solution for a certain class of impulsive neutral functional integrodifferential equations with nonlocal conditions. The results we obtained are a generalization and continuation of the recent resultson this issue.

scholarly journals A method of upper and lower solutions for functional differential inclusions

2002 ◽  
Vol 15 (3) ◽  
pp. 269-276
Author(s):  
Mouffak Benchohra ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
First Order ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

In this paper, a fixed point theorem for condensing maps combined with upper and lower solutions are used to investigate the existence of solutions for first order functional differential inclusions.

scholarly journals Upper and Lower Solutions form-Point Impulsive BVP with One-Dimensionalp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Junfang Zhao ◽  
Jianfeng Zhao ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
First Order ◽  
Impulsive Boundary Value Problems

Upper and lower solutions theories are established for a kind ofm-point impulsive boundary value problems withp-Laplacian. By using such techniques and the Schauder fixed point theorem, the existence of solutions and positive solutions is obtained. Nagumo conditions play an important role in the nonlinear term involved with the first-order derivatives.

MEASURES OF NONCOMPACTNESS IN A SOBOLEV SPACE AND INTEGRO-DIFFERENTIAL EQUATIONS

2016 ◽  
Vol 94 (3) ◽  
pp. 497-506
Author(s):  
REZA ALLAHYARI ◽  
REZA ARAB ◽  
ALI SHOLE HAGHIGHI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Sobolev Space ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Measures Of Noncompactness ◽  
Darbo’S Fixed Point Theorem

The aim of this paper is to introduce a new measure of noncompactness on the Sobolev space$W^{n,p}[0,T]$. As an application, we investigate the existence of solutions for some classes of functional integro-differential equations in this space using Darbo’s fixed point theorem.

scholarly journals Applications of a Fixed Point Result for Solving Nonlinear Fractional and Integral Differential Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 211
Author(s):  
Liliana Guran ◽  
Zoran D. Mitrović ◽  
G. Sudhaamsh Mohan Reddy ◽  
Abdelkader Belhenniche ◽  
Stojan Radenović
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Fractional Differential ◽  
Integral Differential Equations

In this article, we apply one fixed point theorem in the setting of b-metric-like spaces to prove the existence of solutions for one type of Caputo fractional differential equation as well as the existence of solutions for one integral equation created in mechanical engineering.

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