Necessary and sufficient conditions for the existence of non-oscillating and oscillating solutions of quasi-linear functional-differential equations of neutral type with constant coefficients and impulses

Abstract

This paper is dealing with second order quasi-linear impulsive functional-differential equations of neutral type with constant coefficients. Characteristic equations of such equations are established and conditions about the existence of non-oscillating and oscillating solutions in the appropriate form of impulsive exponent or line are obtained.