SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations（a（t）x＇（t））＇＋δ1p（t）x＇（t） ＋δ2q（t）f（x（g（t））） = 0,for 0 ≤ to≤ t, where 51 = ：El and δ±1. The functions p,q,g ： [t0, ∞） → R, f ： R → are continuous, a（t） 〉 0,p（t） ≥0,q（t） 〉 0 for t ≥ to,lirn g（t） = ∞, and q is not identically zero on any subinterval of [to, ∞）. Moreover, the functions q（t）, g（t）, and a（t） are continuously differentiable.

EXISTENCE AND UNIQUENESS OF THE SOLUTION OF A CLASS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

The unicity of the solution, if any, of a class of nonlinear functional differential equations (fde) is established with the help of a transformation. The transformation reduces the fde to an ordinary differential equation. Existence of the solution is established by means of a fixed point theorem.

The Solution to Impulse Boundary Value Problem for a Class of Nonlinear Fractional Functional Differential Equations

In this paper, we investigate the existence of solution for a class of impulse boundary value problem of nonlinear fractional functional differential equation of mixed type. We obtain the existence results of solution by applying some well-known fixed point theorems. An example is given to illustrate the effectiveness of our result.

Contractivity and Exponential Stability of Solutions to Nonlinear Neutral Functional Differential Equations in Banach Spaces

A series of eontractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations （NFDEs） in Banach spaces are obtained, which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations （FDEs）, neutral delay differential equations （NDDEs） and NFDEs of other types which appear in practice.