Stability by Krasnoselskii's theorem in totally nonlinear neutral differential equations
Abstract. In this paper we use fixed point methods to prove asymptotic stability results of the zero solution of a class of totally nonlinear neutral differential equations with functional delay. The study concerns
The equation has proved very challenging in the theory of Liapunov's direct method. The stability results are obtained by means of Krasnoselskii-Burton's theorem and they improve on the work of T.A. Burton (see Theorem 4 in [Liapunov functionals, fixed points, and
stability by Krasnoselskii's theorem, Nonlinear Studies 9 (2001), 181-190]) in which he takes \(c=0\) in the above equation.
Keywords: fixed point, stability, nonlinear neutral equation, Krasnoselskii-Burton theorem.
Mathematics Subject Classification: 47H10, 34K20, 34K30, 34K40.