Almost automorphic mild solutions to some partial neutral functional-differential equations and applications

2008 ◽  
Vol 69 (5-6) ◽  
pp. 1485-1493 ◽  
Author(s):  
Toka Diagana ◽  
Hernán R. Henriquez ◽  
Eduardo M. Hernández
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
Almost Automorphic ◽  
Functional Differential

scholarly journals Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

scholarly journals Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Banach Fixed Point Theorem ◽  
Unified Framework ◽  
Neutral Functional Differential Equations ◽  
Almost Automorphic ◽  
Almost Automorphic Functions

Combining the exponential dichotomy of evolution family, composition theorems for almost automorphic functions with Banach fixed point theorem, we establish new existence and uniqueness theorems for almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain. A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.

scholarly journals ON PSEUDO -ASYMPTOTICALLY PERIODIC FUNCTIONS

2013 ◽  
Vol 87 (2) ◽  
pp. 238-254 ◽  
Author(s):  
MICHELLE PIERRI ◽  
VANESSA ROLNIK
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Periodic Functions ◽  
Qualitative Properties ◽  
Neutral Functional Differential Equations ◽  
Asymptotically Periodic ◽  
Functional Differential ◽  
Equations With Delay

AbstractWe introduce the concept of pseudo$ \mathcal{S} $-asymptotically periodic functions and study some of the qualitative properties of functions of this type. In addition, we discuss the existence of pseudo$ \mathcal{S} $-asymptotically periodic mild solutions for abstract neutral functional differential equations. Some applications involving ordinary and partial differential equations with delay are presented.

scholarly journals EXISTENCE OF SOLUTIONS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

1999 ◽  
Vol 30 (4) ◽  
pp. 299-309
Author(s):  
K. BALACHANDRAN ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Cosine Families ◽  
Functional Differential

Sufficient conditions for existence of mild solutions for second order neutral functional differential equations are established by using the theory of strongly continuous cosine families and the Schaefer theorem.

scholarly journals EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

2008 ◽  
Vol 78 (3) ◽  
pp. 365-382 ◽  
Author(s):  
HERNÁN R. HENRÍQUEZ ◽  
MICHELLE PIERRI ◽  
PLÁCIDO TÁBOAS
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Qualitative Properties ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Bounded Continuous Function ◽  
Functional Differential

AbstractA bounded continuous function $u:[0,\infty )\to X$ is said to be S-asymptotically ω-periodic if $ \lim _{t\to \infty }[ u(t+\omega ) -u(t)]=0$. This paper is devoted to study the existence and qualitative properties of S-asymptotically ω-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given.

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