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 solution of a system of differential equations using generalized Darbo's fixed point theorem

2021 ◽  
Vol 6 (12) ◽  
pp. 13358-13369
Author(s):  
Rahul ◽  
◽  
Nihar Kumar Mahato
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solution ◽  
System Of Differential Equations ◽  
Darbo’S Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

<abstract><p>In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.</p></abstract>

scholarly journals On fuzzy Volterra integral equations with deviating arguments

2004 ◽  
Vol 2004 (2) ◽  
pp. 169-176 ◽  
Author(s):  
K. Balachandran ◽  
P. Prakash
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Volterra Integral Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We investigate the problem of existence of solutions of fuzzy Volterra integral equations with deviating arguments. The results are obtained by using the Darbo fixed point theorem.

scholarly journals An existence theorem for nonlinear delay differential equations

1989 ◽  
Vol 2 (2) ◽  
pp. 85-89
Author(s):  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

In this paper we prove a theorem on the existence of solutions of nonlinear delay differential equations, with implicit derivatives. The result is established using the measure of noncompactness of a set and Darbo's fixed point theorem.

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.

Initial Value Problem of Fractional Integro-Differential Equations in Banach Space

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Adel Jawahdou
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Initial Value

AbstractThis paper is devoted to study the existence of solutions of nonlinear fractional integro-differential equation, via the techniques of measure of noncompactness. The investigation is based on a Schauder's fixed point theorem. The main result is less restrictive than those given in the literature. An illustrative example is given.

scholarly journals On the existence of solutions for non-linear functional integral equation

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 17-23
Author(s):  
E.M. El-Abd
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Darbo Fixed Point Theorem

We have proved the existence of monotonic solutions of a nonlinear functional integeral equation by using Darbo fixed point theorem associated with a measure of noncompactness.

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 nonoscillatory solutions of higher order neutral differential equations

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2147-2153 ◽  
Author(s):  
T. Candan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments

This article is concerned with nonoscillatory solutions of higher order nonlinear neutral differential equations with deviating and distributed deviating arguments. By using Knaster-Tarski fixed point theorem, new sufficient conditions are established. Illustrative example is given to show applicability of results.

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