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

cited authors

  • Gal, CG

authors

abstract

  • 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.

publication date

  • January 1, 2006

Digital Object Identifier (DOI)

start page

  • 1

end page

  • 8