scholarly journals Existence and uniqueness of solutions of a semilinear functional-differential evolution nonlocal Cauchy problem

2000 ◽  
Vol 13 (2) ◽  
pp. 171-179
Author(s):  
Katarzyna Kolodziej
Keyword(s):  
Cauchy Problem ◽  
Differential Evolution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Uniqueness Of Solutions ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

Two theorems about the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution nonlocal Cauchy problem in a general Banach space are proved. Methods of semigroups and the Banach contraction theorem are applied.

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 a mild solution of a semilinear functional-differential evolution nonlocal problem

1997 ◽  
Vol 10 (3) ◽  
pp. 265-271 ◽  
Author(s):  
Ludwik Byszewski ◽  
Haydar Akca
Keyword(s):  
Differential Evolution ◽  
Mild Solution ◽  
Continuous Dependence ◽  
Nonlocal Problem ◽  
Semigroup Of Operators ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional-differential evolution equation in a general Banach space are studied. Methods of a C0 semigroup of operators and the Banach contraction theorem are applied. The result obtained herein is a generalization and continuation of those reported in references [2-8].

scholarly journals Impulsive functional-differential equations with nonlocal conditions

2002 ◽  
Vol 29 (5) ◽  
pp. 251-256 ◽  
Author(s):  
Haydar Akça ◽  
Abdelkader Boucherif ◽  
Valéry Covachev
Keyword(s):  
Continuous Dependence ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Semigroup Of Operators ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The existence, uniqueness, and continuous dependence of a mild solution of an impulsive functional-differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of aC0semigroup of operators and the Banach contraction theorem are applied.

scholarly journals On Some Qualitative Properties of Mild Solutions of Nonlocal Semilinear Functional Differential Equations

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Rupali S. Jain ◽  
M. B. Dhakne
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Qualitative Properties ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Banach Contraction Theorem ◽  
Equations With Delay

AbstractIn the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

Some Uniqueness Results for Impulsive Semilinear Neutral Functional Differential Equations

2002 ◽  
Vol 9 (3) ◽  
pp. 423-430
Author(s):  
M. Benchohra ◽  
A. Ouahabi
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Functional Differential ◽  
The Banach Contraction Principle

Abstract The Banach contraction principle is used to investigate the existence and uniqueness of solutions for first and second order impulsive semilinear neutral functional differential equations in Banach spaces.

scholarly journals Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alberto Cabada ◽  
Om Kalthoum Wanassi
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Part ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Exhaustive Study ◽  
The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

scholarly journals Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuqi Wang ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Novel Approach ◽  
Banach Contraction ◽  
Left And Right ◽  
Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

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