On Oscillatory to Nonlinear Impulsive Differential Equation of Second-Order with Damping Term

Abstract

The paper focuses on the sufficient conditions for oscillatory property to the nonlinear impulsive differential equation(IDE) of the second order with damping term. We submitted a suitable impulsive conditions with the nonlinear equation. The obtained new results in this article generalize and extend some modification results to linear (IDEs) with damping term in the references. We have been given illustrative example to apply the conditions in the main results.

On the Existence and Oscillatory Solutions of Multiple Delay Differential Equation

“…The consideration of theory of differential equations (DEs) includes several fields of study such as the existence of solutions [1,2], numerical solutions [3,4], and the finding the qualitative properties [5,6].…”

Existence and Qualitative Property of Differential Equation with Delayed Arguments

“…(1.1) for 𝜉 ≽ 𝜉 1 . We say that solution 𝜒(𝜉) is a nonoscillatory solution if it is eventually negative or eventually positive, so there exists 𝜉 * ≽ 𝜉 0 , such that 𝜒(𝜉) ≻ 0 or 𝜒(𝜉) ≺ 0 for all 𝜉 ≽ 𝜉 * , otherwise the solution is said to be oscillatory [6]. We need the following lemma and theorem in the main results of second section.…”