On oscillatory first order neutral impulsive difference equations. (English) Zbl 07286018

Tripathy, Arun Kumar; Chhatria, Gokula Nanda

Math. Bohem. 145, No. 4, 361-375 (2020).

In this work, main objective is to study the oscillatory behaviour of the solutions of the system \[\triangle(y(n)+p(n)y(n-\tau))+q(n)F(y(n-\sigma))=0\] where \(p,q\) are real valued functions with discrete arguments such that \(q(n)>0,|p(n)|<\infty\) for \(n\in\mathbb{N}(n_0)=\{n_0,n_0+1,\dots\},F\in C(\mathbb{R},\mathbb{R})\) satisfying the property \(xF(x)>0\) for \(x\ne 0\) and \(\triangle\) is the forward difference operator defined by \(\triangle u(n)=u(n+1)-u(n)\). And \(m_1,m_2,m_3,\dots\) be the moments of impulsive effect with the property \(0<m_1<m_2<\dots,\lim_{j\rightarrow\infty}m_j=\infty\). Authors established sufficient conditions for oscillation of a class of first order neutral impulsive difference equations with deviating arguments and fixed moments of impulsive effect.

Reviewer: Haydar Akca (Abu Dhabi)

MSC:

39A10	Additive difference equations
39A12	Discrete version of topics in analysis

Keywords:

oscillation; nonoscillation; impulsive difference equation; nonlinear neutral difference equation; delay

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