Abstract
This paper is devoted to the existence of a periodic solution for ϕ-Laplacian neutral differential equation as follows
$$\begin{array}{}
(\phi(x(t)-cx(t-\tau))')'=f(t,x(t),x'(t)).
\end{array}$$
By applications of an extension of Mawhin’s continuous theorem due to Ge and Ren, we obtain that given equation has at least one periodic solution. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature.
Some a priori bounds for solutions of the constant Gauss curvature equation