On Forced Impulsive Oscillatory Nonlinear Neutral Systems of the Second Order

We study the oscillatory and nonoscillatory behavior of solutions a class forced impulsive nonlinear neutral differential systems form $$ \left\{\begin{array}{c}{\left(r(t){\left(y(t)+p(t)y\left(t-\tau \right)\right)}^{\prime}\right)}^{\prime }+q(t)G\left(y\left(t-\sigma \right)\right)=f(t),\kern1.75em t\ne {\tau}_k,\kern0.75em k\ \epsilon\ \mathbb{N},\\ {}\Delta \left(r\left({\tau}_k\right){\left(y\left({\tau}_k\right)+p\left({\tau}_k\right)y\left({\tau}_k-\tau \right)\right)}^{\prime}\right)+h\left({\tau}_k\right)G\left(y\left({\tau}_k-\sigma \right)\right)=\mathrm{g}\left({\tau}_k\right),\kern0.75em \mathbb{N},\end{array}\right. for various ranges values p.t /: Sufficient conditions existence positive bounded this system are also obtained.