Fixed points and stability in nonlinear neutral Volterra integro-differential equations with variable delays

Fixed Points and Stability in Nonlinear Neutral Volterra Integro-differential Equations with Variable Delays

Abstract. In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a necessary and sufficient condi...

Fixed Points and Stability in Neutral Nonlinear Differential Equations with Variable Delays

Abstract. By means of Krasnoselskii’s fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307–3315], and also those of T.A. Burton [Fixed ...

Fixed Points and Stability in Nonlinear Equations with Variable Delays

Fixed points and stability in differential equations with variable delays

In this paperwe consider a linear scalar differential equationwith variable delays andgive conditions to ensure that the zero solution is asymptotically stable bymeans of fixedpoint theory.These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. 2...

Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays