Trichotomy of nonoscillatory solutions for nonlinear first- order neutral difference equation with generalized difference operators - Bolat, Yaşar; Gevgeşoğlu, Murat (Gazi University Journal of Science, 2025)
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: Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler; Ordinary Differential Equations, Difference Equations and Dynamical Systems; Trichotomy; Oscillation; Nonoscillation; Neutral difference equation; Generalized difference operators.