Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
Article
Gal, CG. (2006). Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
. 1-8. 10.14232/ejqtde.2006.1.16
Gal, CG. (2006). Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
. 1-8. 10.14232/ejqtde.2006.1.16
In this paper we consider the semilinear differential equation with deviated argument in a Fréchet space x′(t) = Ax(t) + f(t,x(t),x[α(x(t),t)]), t ∈ ℝ, where A is the infinitesimal (bounded) generator of a C0-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions f and α we prove the existence and uniqueness of an almost automorphic mild solution to the equation.