scholarly journals Exact Controllability of an Impulsive Semilinear System with Deviated Argument in a Banach Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Sanjukta Das ◽  
Dwijendra N. Pandey ◽  
N. Sukavanam
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Semigroup Theory ◽  
Exact Controllability ◽  
Impulsive Conditions ◽  
Banach Contraction ◽  
Deviated Argument ◽  
Functional Differential

A functional differential equation with deviated argument coupled with impulsive conditions is studied for the existence and uniqueness of the mild solution and exact controllability of the system. The results are obtained by using Banach contraction principle and C0 semigroup theory without imposing additional assumptions such as analyticity and compactness conditions on the generated semigroup and the nonlinear term. An example is provided to illustrate the presented theory.

scholarly journals Existence results of noninstantaneous impulsive fractional integro-differential equation

2020 ◽  
Vol 53 (1) ◽  
pp. 373-384 ◽  
Author(s):  
Haribhai R. Kataria ◽  
Prakashkumar H. Patel ◽  
Vishant Shah
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

Abstract Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.

scholarly journals Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
T. E. Govindan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Local Lipschitz Condition ◽  
Functional Differential ◽  
Special Case ◽  
Partial Functional Differential Equation

This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

scholarly journals Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 213-219 ◽  
Author(s):  
D. Bahuguna
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Regularity Of Solutions ◽  
Retarded Differential Equation ◽  
Retarded Differential Equations

In the present work, we consider a semilinear retarded differential equation in a Banach space. We first establish the existence and uniqueness of a mild solution and then prove its regularity under different additional conditions. Finally, we consider some applications of the abstract results.

Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3381-3395 ◽  
Author(s):  
Renu Chaudhary ◽  
Dwijendra Pandey
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Semigroup Theory ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, Monotone iterative technique coupled with the method of lower and upper solutions is employed to discuss the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.

scholarly journals Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem

1999 ◽  
Vol 12 (1) ◽  
pp. 91-97 ◽  
Author(s):  
Ludwik Byszewski
Keyword(s):  
Cauchy Problem ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Special Kind ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Picard Method ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.

scholarly journals On the Controllability of a Differential Equation with Delayed and Advanced Arguments

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Raúl Manzanilla ◽  
Luis Gerardo Mármol ◽  
Carmen J. Vanegas
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Infinitesimal Generator ◽  
Semigroup Theory ◽  
Exact Controllability

A semigroup theory for a differential equation with delayed and advanced arguments is developed, with a detailed description of the infinitesimal generator. This in turn allows to study the exact controllability of the equation, by rewriting it as a classical Cauchy problem.

scholarly journals Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Cheng-Min Su ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Fractional Differential

In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional differential equation: D0+qCut=ft,ut,  t∈0,1, u0=u′′0=0,  D0+σ1Cu1=λI0+σ2u1, where 2<q<3, 0<σ1≤1, σ2>0, and λ≠Γ2+σ2/Γ2-σ1. The main tools used are nonlinear alternative of Leray-Schauder type and Banach contraction principle.

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