Stability and boundedness in functional differential equations (Q1076894)

The author studies stability and boundedness of the solutions of the functional differential equation with infinite delay \(\dot x(t)=f(t,x_ t)\) by employing the theory of Lyapunov-Razumikhin type. First a fundamental comparison theorem used in this paper is stated. Next stability and boundedness are discussed, and finally some applications of the results obtained in this paper to the integrodifferential equation of Volterra type \[ \dot x(t)=A(t)x(t)+\int^{t}_{0}k(t,s,x(s))ds+f(t,x_ t) \] are presented.