In this work, the authors have discussed necessary and sufficient conditions for oscillation asymptotic behaviour of solutions second order nonlinear (sublinear/superlinear) neutral impulsive difference equations. The results are illustrated with examples under suitable fixed moments effect.

Differential equations are useful mathematical tools for solving complex problems. include ordinary and partial differential equations. Nonlinear can express the nonlinear relationship between dependent independent variables. The second-order neutral studied in this paper a class of quadratic differentiable that delay terms. According to t-value interval equation function, basis is needed selec...

Abstract: In this paper existence of mild solution of a class of second order partial neutral differential equation with state dependent delay and non-instantaneous impulses is investigated. Hausdorff measure of noncompactness and Darbo Sadovskii fixed point theorem are used to prove the existence. Also, some restrictive conditions such as the compactness assumption on the associated cosine or ...