On the existence of nonoscillatory solutions of third-order nonlinear differential equations

Abstract The aim of this paper is to study the qualitative properties of solutions of nonlinear differential equations of the third-order with quasiderivatives. Nonoscillatory solutions of investigated equations are divided into several classes according to their asymptotic behavior as t tends to infinity. We present the necessary and sufficient conditions for the existence of solutions in these classes. Sufficient conditions are proved via a topological approach based on the Schauder fixed point theorem.

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