Trichotomy of nonoscillatory solutions for nonlinear first- order neutral difference equation with generalized difference operators

Year 2025, Early View, 1 - 1

Yaşar Bolat , Murat Gevgeşoğlu

Abstract

In this study, we examine the trichotomy of non-oscillatory solution for the nonlinear first-order neutral difference equation
∆_a (x_n-a^(n+1) x_(n-1) )+∆_a (x_(n-1)/b_(n-1) )+q_n f(x_(n-τ) )=0,n∈N_max{1,τ} ,
where ∆_a x_n=x_(n+1)-ax_n,τ∈N,a∈R^+ with ∆_a^m Δ=∆_a^(m-1) (∆_a ), aⁿ is a general term of exponential sequence, (q_n) is real valued sequences. The accuracy of the primary findings is demonstrated by examples.

Keywords

Trichotomy, Oscillation, Nonoscillation, Neutral difference equation, Generalized difference operators.

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