Differential equations are useful mathematical tools for solving complex problems. include ordinary and partial differential equations. Nonlinear can express the nonlinear relationship between dependent independent variables. The second-order neutral studied in this paper a class of quadratic differentiable that delay terms. According to t-value interval equation function, basis is needed selec...

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...

Sufficient conditions are obtained for every solution of first order nonlinear neutral delay forced impulsive differential equations with positive and negative coefficients tends to a constant as t ∞.

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations (a(t)x′(t))′ + f(t, x(g(t))) = 0, t ≥ t0 (a(t)(x(t)− p(t)x(t− τ))′)′ + f(t, x(g(t))) = 0, t ≥ t0 . Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.

This paper is a survey of the recent results of the author on the stability of linear and nonlinear neutral type functional differential equations. Mainly, vector equations are considered. In particular, equations whose nonlinearities are causal mappings are investigated. These equations include neutral type, ordinary differential, differential-delay, integro-differential and other traditional ...

In this paper we study the existence of solutions for the initial value problem for functional differential equations, as well as, for neutral functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis. AMS (MOS) Subject Classification. 26A33, 26A42, 34K30