Sufficient conditions for the existence of some nonoscillatory solutions of third-order nonlinear differential equations

The aim of this paper is to study the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the sufficient conditions ensuring the existence of some nonoscillatory solutions with a specified asymptotic property as tt tends to infinity. The basic tool used in proving our results is the classical Banach contraction mapping principle.