Asymptotic behavior of positive solutions of fourth-order nonlinear difference equations - Agarwal, P.; Manojlović, J. V. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We consider a class of fourth-order nonlinear difference equations of the form Δ^2(p_n(Δ^2y_n)^α)+q_n y^β_n+3=0, nN where α, β are the ratios of odd positive integers, and {p_n}, {q_n} are positive real sequences defined for all nN . We establish necessary and sufficient conditions for the existence of nonoscillatory solutions with specific asymptotic behavior under suitable combinations of the convergence or divergence conditions of the sums _n=n_0^∞np_n^1/α and_n=n_0^∞(np_n)^1/α.