Almost periodic solutions of neutral functional differential equations with nonautonomous operator (Q1905715)

Neutral functional differential systems of the form \[ d/dt D(t) x_t= f(t, x_t)+ g(t, x_t)\tag{1} \] and \(D(t) F= F(0)- \int^0_{- r} [d_\theta \mu(t+ s)] F(\theta)\), \(|\int^0_{- s} [d_\theta\mu(t+ \theta)|\leq l(s) \sup_{- s\leq \theta\leq 0} |F(\theta)|\) are investigated. Some existence theorems on almost periodic solutions for almost periodic equations (1) are obtained. The demonstrations are based on Lyapunov functionals. The results extend some earlier results mentioned in the paper.