On nonoscillatory solutions tending to zero of third-order nonlinear differential equations

Abstract

ABSTRACT. The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.

Existence of nonoscillatory solutions tending to zero of fourth-order nonlinear neutral dynamic equations on time scales

“…Therefore, new methods should be found to study nonoscillatory solutions tending to zero of the equations. Mojsej and Tartal'ová [23] were concerned with a third-order nonlinear differential equation…”

“…Inspired by [23], Qiu [24] investigated the nonoscillatory solutions tending to zero of (2) when g(t) ≥ t for t ∈ [t 0 , ∞) T , by employing a Banach space…”