POSITIVE PERIODIC SOLUTIONS OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH
NONLINEAR NEUTRAL TERM
Abstract
\begin{abstract} In this work, we discuss the existence
of positive periodic solutions of a class of second order nonlinear
neutral delay differential equations of the form
\\ \begin{align*} &
[u(t)-p(t)f(u(t-\alpha))-q(t)g(u(t-\beta))]’‘=
-\sigma(t) u(t)+ h(t, u(t-\alpha),
u(t-\beta))\\ &
[u(t)-p(t)f(u(t-\alpha))-q(t)g(u(t-\beta))]”=
\sigma(t) u(t)- h(t, u(t-\alpha),
u(t-\beta)) \end{align*} by using
Krasnoselskii’s fixed point theorem. \\
{\bf{Mathematics subject classification (2010)}}:
34K13, 34A34\\
{\bf{Keywords}:} Periodic solution, neutral
differential equation, delay, nonlinear.\\
\\ \end{abstract}