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
2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zhanrong Hu ◽  
Zhen Jin

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.


2013 ◽  
Vol 87 (2) ◽  
pp. 238-254 ◽  
Author(s):  
MICHELLE PIERRI ◽  
VANESSA ROLNIK

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.


1999 ◽  
Vol 30 (4) ◽  
pp. 299-309
Author(s):  
K. BALACHANDRAN ◽  
S. MARSHAL ANTHONI

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.


2008 ◽  
Vol 78 (3) ◽  
pp. 365-382 ◽  
Author(s):  
HERNÁN R. HENRÍQUEZ ◽  
MICHELLE PIERRI ◽  
PLÁCIDO TÁBOAS

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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