Existence and uniqueness of solutions of a semilinear differential equation

2003 ◽  
Vol 52 (5) ◽  
pp. 1251-1263 ◽  
Author(s):  
Mats Anders Olofsson
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Semilinear Differential Equation

scholarly journals About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Irina Volinsky
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Uniqueness Of Solutions ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

The impulsive delay differential equation is considered(Lx)(t)=x′(t)+∑i=1mpi(t)x(t-τi(t))=f(t), t∈[a,b],  x(tj)=βjx(tj-0), j=1,…,k, a=t0<t1<t2<⋯<tk<tk+1=b, x(ζ)=0, ζ∉[a,b],with nonlocal boundary conditionlx=∫abφsx′sds+θxa=c,  φ∈L∞a,b;  θ, c∈R.Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained.

scholarly journals Complex Transforms for Systems of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We provide a complex transform that maps the complex fractional differential equation into a system of fractional differential equations. The homogeneous and nonhomogeneous cases for equivalence equations are discussed and also nonequivalence equations are studied. Moreover, the existence and uniqueness of solutions are established and applications are illustrated.

Inverse problems of mixed type in linear plate theory

2004 ◽  
Vol 15 (2) ◽  
pp. 129-146 ◽  
Author(s):  
DOMINGO SALAZAR ◽  
REX WESTBROOK
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Plate Theory ◽  
Order Partial Differential Equation ◽  
General Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Sag Bending

The characterisation of those shapes that can be made by the gravity sag-bending manufacturing process used to produce car windscreens and lenses is modelled as an inverse problem in linear plate theory. The corresponding second-order partial differential equation for the Young's modulus is shown to change type (possibly several times) for certain target shapes. We consider the implications of this behaviour for the existence and uniqueness of solutions of the inverse problem for some frame geometries. In particular, we show that no general boundary conditions for the inverse problem can be prescribed if it is desired to achieve certain kinds of target shapes.

scholarly journals Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Karim Guida ◽  
Lahcen Ibnelazyz ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

Periodic Problem for the Generalized Basset Fractional Differential Equation

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Svatoslav Stanĕk
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Problem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

AbstractWe discuss the existence and uniqueness of solutions to the periodic fractional problem u′ = A

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