On the existence of positive solutions of a state-dependent neutral functional differential equation with two state-delay functions

In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.

Positive periodic solutions for singular high-order neutral functional differential equations

In this paper, we establish new results on the existence of positive periodic solutions for the following high-order neutral functional differential equation (NFDE) $$\begin{array}{} (x(t)-cx(t-\sigma)) ^{(2m)}+f(x(t)) x'(t)+g(t,x(t-\delta))=e(t). \end{array}$$ The interesting thing is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the corresponding ones known in the literature. Two examples are given to illustrate the effectiveness of our results.