Existence of bounded and unbounded nonoscillatory solutions of nonlinear partial difference equations

Abstract: Consider the higher order nonlinear partial difference equation of neutral type where , , and . In this paper, we first establish the discrete Arzela–Ascoli''s theorem. Next, we obtain some sufficient conditions for the existence of bounded and unbounded nonoscillatory solution of Eq. (∗). [Copyright &y& Elsevier]