Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory

Stability in Nonlinear Neutral Differential Equations with Variable Delays Using Fixed Point Theory

Abstract. The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient functions to change sign and do not require bounded delays. The obtained results improve an...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Stability in neutral nonlinear differential equations with functional delays using fixed-point theory

We use fixed point theorems to obtain stability results about the trivial solution of the nonlinear neutral differential equation with functional delay x′(t) = −a(t)x(t) + c(t)x′(t− g(t)) + q(x(t), x(t− g(t)) AMS Subject Classifications: 34K20, 45J05, 45D05

existence of periodic solutions in totally nonlinear neutral differance equations with variable delay

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...