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

Consider the first-order neutral nonlinear difference equation of the form View the MathML source , 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∞nqnΣj=n∞qj = ∞ commonly used in the literature.