%0 Journal Article
%T Existence and uniform asymptotic stability for an abstract differential equation with infinite delay
%A Cung The Anh
%A Le Van Hieu
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X Using the Contraction Mapping Principle, we study the existence, uniqueness, and uniform asymptotic stability of solutions to an abstract differential equation with infinite delay of the form $du(t)/dt+Au(t)=B(t,u_t)$, where A is a positive sectorial operator and the nonlinear part B is Lipschitz continuous with respect to a fractional power of A in the second variable and the Lipschitz coefficient may depend on time t. Some special cases and examples are provided to illustrate the results obtained.
%K Infinite delay
%K sectorial operator
%K mild solution
%K uniform asymptotic stability
%K fixed point method
%U http://ejde.math.txstate.edu/Volumes/2012/51/abstr.html