ASYMPTOTIC TRICHOTOMY OF SOLUTIONS OF A CLASS OF EVEN ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH QUASIDIFFERENCES

We consider a class of higher order nonlinear neutral difference equations with quasidifferences where sequence (p(n)) is a real sequence. The classification of nonoscillatory solutions of this equation are obtained. For a class of even order nonlinear neutral difference equations, dependent on (p(n)), the conditions under which the eventually positive solutions of the equation can be classified into three nonempty distinct categories are given. We present sufficient condition under which the equation has a solution which converges to zero as well necessary and sufficient conditions under which the equation has a solution which tends to a nonzero constant and which diverges to infinity.