Study on the oscillation of solution to second-order impulsive systems

Abstract

In the present article, we set the if and only if conditions for the solutions of the class of neutral impulsive delay second-order differential equations. We consider two cases when it is non-increasing and non-decreasing for quotient of two positive odd integers. Our main tool is the Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.

Keywords

• nonlinear
• nonoscillation
• delay argument
• second-order differential equation
• lebesgue's dominated convergence theorem