Adjoint Semigroup Theory for a Class of Functional Differential Equations

1976 ◽  
Vol 7 (5) ◽  
pp. 729-745 ◽  
Author(s):  
J. A. Burns ◽  
T. L. Herdman
Keyword(s):  
Differential Equations ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Adjoint Semigroup ◽  
Functional Differential

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.

Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces

2010 ◽  
Vol 17 (3) ◽  
pp. 423-436 ◽  
Author(s):  
Selma Baghli ◽  
Mouffak Benchohra
Keyword(s):  
Differential Equations ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Fréchet Spaces ◽  
Evolution Operators ◽  
Neutral Functional Differential Equations ◽  
Nonlinear Alternative ◽  
Unique Mild Solution ◽  
Contractive Maps ◽  
Functional Differential

Abstract The existence of a unique mild solution on a semiinfinite interval for a first order semilinear neutral functional differential equations involving evolution operators in Fréchet spaces is investigating using a nonlinear alternative of Leray–Schauder type for contractive maps, combined with semigroup theory.

Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in Lp Spaces

2010 ◽  
Vol 62 (1) ◽  
pp. 74-93 ◽  
Author(s):  
Arnaud Ducrot ◽  
Zhihua Liu ◽  
Pierre Magal
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Explicit Formulas ◽  
Neutral Functional Differential Equations ◽  
Lp Spaces ◽  
Linear Problems ◽  
Functional Differential ◽  
Densely Defined

AbstractWe present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) in Lp spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the NFDE as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems.

scholarly journals Exponential Stability in Mean Square for Neutral Stochastic Partial Functional Differential Equations with Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Nan Ding
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Mild Solution ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Partial Functional Differential Equations ◽  
Functional Differential ◽  
Stability In Mean Square

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. Finally, an example is provided to illustrate the obtained theory.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

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