scholarly journals Nonautonomous partial functional differential equations; existence and regularity

2017 ◽  
Vol 4 (1) ◽  
pp. 108-127 ◽  
Author(s):  
Moussa El-Khalil Kpoumiè ◽  
Khalil Ezzinbi ◽  
David Békollè
Keyword(s):  
Differential Equations ◽  
Linear Part ◽  
Functional Differential Equations ◽  
Local Existence ◽  
Sufficient Conditions ◽  
Reaction Diffusion Equation ◽  
Regularity Of Solutions ◽  
Partial Functional Differential Equations ◽  
Strict Solutions ◽  
Functional Differential

Abstract The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring the existence of the strict solutions. Finally, we consider a reaction diffusion equation with delay to illustrate the obtained results.

scholarly journals OSCILLATION OF PARTIAL FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

1995 ◽  
Vol 26 (2) ◽  
pp. 131-139
Author(s):  
NORIO YOSHIDA
Keyword(s):  
Differential Equations ◽  
Parabolic Equations ◽  
Hyperbolic Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cylindrical Domain ◽  
Deviating Arguments ◽  
Partial Functional Differential Equations ◽  
All Solutions ◽  
Functional Differential

A class of partial functional-differential equations with deviating argu- ments including parabolic equations, hyperbolic equations and·beam equations is studied, and sufficient conditions are derived for all solutions of certain boundary value problem to be oscillatory in a cylindrical domain.

scholarly journals Almost periodic mild solutions of a class of partial functional differential equations

1998 ◽  
Vol 3 (3-4) ◽  
pp. 425-436 ◽  
Author(s):  
Bernd Aulbach ◽  
Nguyen Van Minh
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Partial Functional Differential Equations ◽  
Semilinear Equation ◽  
Functional Differential ◽  
Lipschitz Conditions

We study the existence of almost periodic mild solutions of a class of partial functional differential equations via semilinear almost periodic abstract functional differential equations of the form(*)                                                                       x′=f(t,x,xt).To this end, we first associate with every almost periodic semilinear equation(**)                                                                       x′=F(t,x).a nonlinear semigroup in the space of almost periodic functions. We then give sufficient conditions (in terms of the accretiveness of the generator of this semigroup) for the existence of almost periodic mild solutions of (**) as fixed points of the semigroup. Those results are then carried over to equation (*). The main results are stated under accretiveness conditions of the functionfin terms ofxand Lipschitz conditions with respect toxt.

scholarly journals Global Attractor for Partial Functional Differential Equations with State-Dependent Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhimin He ◽  
Bo Du
Keyword(s):  
Differential Equations ◽  
Global Attractor ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Global Attractors ◽  
Partial Functional Differential Equations ◽  
State Dependent ◽  
Classic Theory ◽  
State Dependent Delay ◽  
Functional Differential

This work aims to investigate the existence of global attractors for a class of partial functional differential equations with state-dependent delay. Using the classic theory about global attractors in infinite dimensional dynamical systems, we obtain some sufficient conditions for guaranteeing the existence of a global attractor.

scholarly journals Periodic solutions for some partial functional differential equations

2004 ◽  
Vol 2004 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Rachid Benkhalti ◽  
Khalil Ezzinbi
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Bounded Solution ◽  
Linear Part ◽  
Functional Differential Equations ◽  
Nonlinear Case ◽  
Partial Functional Differential Equations ◽  
Functional Differential

We study the existence of a periodic solution for some partial functional differential equations. We assume that the linear part is nondensely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove the existence of a periodic solution under the existence of a bounded solution. In the nonlinear case, using a fixed-point theorem concerning set-valued maps, we establish the existence of a periodic solution.

scholarly journals On variational formulations for functional differential equations

2007 ◽  
Vol 5 (1) ◽  
pp. 89-101 ◽  
Author(s):  
I. A. Kolesnikova ◽  
A. M. Popov ◽  
V. M. Savchin
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Variational Principles ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Partial Functional Differential Equations ◽  
Functional Differential ◽  
Necessary And Sufficient ◽  
Variational Formulations

Necessary and sufficient conditions for the existence of integral variational principles for boundary value problems for given ordinary and partial functional differential equations are obtained. Examples are given illustrating the results.

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.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

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