Oscillation criteria for first-order neutral nonlinear difference equations with variable coefficients

AbstractConsider the first-order neutral nonlinear difference equation of the form δ (yn−pnyn−r)+ qn ∏i=lm |yn−σi|ai sgn yn−σi = 0, n=0,1,…, where τ > 0, σi ≥ 0 (i = 1, 2,…, m) are integers, {pn} and {qn} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Σn=0∞ qn = ∞ or Σn=0∞ nqn Σj=n∞ qj = ∞ commonly used in the literature