# Necessary and sufficient conditions for oscillation of solutions to second-order neutral differential equations with impulses

In: Tatra Mountains Mathematical Publications, vol. 76, no. 2
Shyam Sundar Santra
Detaily:
Rok, strany: 2020, 157 - 170
Jazyk: eng
Kľúčové slová:
oscillation, non-oscillation, neutral, delay, Lebesgue's Dominated Convergence theorem, impulses.
Typ článku: Mathematics - Dynamical Systems and their Applications
Typ dokumentu: Scientific paper
O článku:
In this work, necessary and sufficient conditions for oscillation of solutions of second-order neutral impulsive differential system

\begin{eqnarray*} \{\begin{array}{lcl} \big(r(t)(z'(t))γ\big)' + q(t)xα\big(σ(t)\big)=0, && t≥ t0, t\neq λk, Δ \big(r(λk)(z'(λk))γ\big) + h(λk)xα \big(σ(λk)\big)=0, && k \in \mathbb{N} \end{array} . \end{eqnarray*}

are established, where

$$z(t)=x(t)+p(t)x\big(τ(t)\big).$$

Under the assumption $\int\big(r(η)\big)-1/α \mathrm{d}η = ∞$, two cases when $γ > α$ and $γ < α$ are considered. The main tool is Lebesgue's Dominated Convergence theorem. Examples are given to illustrate the main results, and state an open problem.

Ako citovať:
ISO 690:
Santra, S. 2020. Necessary and sufficient conditions for oscillation of solutions to second-order neutral differential equations with impulses. In Tatra Mountains Mathematical Publications, vol. 76, no.2, pp. 157-170. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0025

APA:
Santra, S. (2020). Necessary and sufficient conditions for oscillation of solutions to second-order neutral differential equations with impulses. Tatra Mountains Mathematical Publications, 76(2), 157-170. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0025
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 20. 10. 2020
Verejná licencia: