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

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.

### MSC:

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

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