Abstract:
The aim of this paper is to consider singular third-order functional
differential equations with
$p$-Laplacianlike operator of the form
$$
(\varphi_p (x''(t)))' +f(t,x(t-\tau))=e(t).
$$
Unlike in previous works,
$f$
has a strong singularity at
$x=0$
and
satisfies a small force condition at
$ x=\infty$.
Based on a continuation theorem due to
Mawhin, new results on the existence
of positive periodic solutions are obtained, which makes it possible to refine and extend
some related results in the literature.
A typical example demonstrating the effectiveness and flexibility of the
main results is given.
