Geodesic
Existence and stability of solutions to neutral equations with infinite delay
Electronic journal of differential equations, Tome 2013 (2013)
In this article, by using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and alpha-norm is used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. A stability result for the autonomous case is also established. We conclude with an example that illustrates the applications of the results obtained.
Classification : 34K25, 34K30, 34G20
Keywords: neutral functional differential equation, analytic semigroup, fractional power operator, linearized stability, infinite delay 
@article{EJDE_2013__2013__a11,
     author = {Fu,  Xianlong},
     title = {Existence and stability of solutions to neutral equations with infinite delay},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1293.34103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a11/}
}
TY  - JOUR
AU  - Fu,  Xianlong
TI  - Existence and stability of solutions to neutral equations with infinite delay
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a11/
LA  - en
ID  - EJDE_2013__2013__a11
ER  - 
%0 Journal Article
%A Fu,  Xianlong
%T Existence and stability of solutions to neutral equations with infinite delay
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a11/
%G en
%F EJDE_2013__2013__a11
Fu,  Xianlong. Existence and stability of solutions to neutral equations with infinite delay. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a11/