ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH-ORDER NONLINEAR DIFFERENCE EQUATIONS

We consider a class of fourth-order nonlinear difference equations of the form Delta(2)(p(n)(Delta(2)y(n))(alpha)) + q(n)y(n+3)(beta) = 0, n is an element of N, where alpha, beta are ratios of odd positive integers and {p(n)}, {q(n)} are positive real sequences defined for all n is an element of N(n(0)). We establish necessary and sufficient conditions for the existence of nonoscillatory solutions with specific asymptotic behavior under suitable combinations of convergence or divergence conditions for the sums Sigma(infinity)(n=n0) n/p(n)(1/alpha) and Sigma(infinity)(n=n0) (n/p(n))(1/alpha).