Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

Article type: Research Article

Authors: Vetro, Calogero^a | Wardowski, Dariusz^{b; *}

Affiliations: [a] Department of Mathematics and Computer Science, University of Palermo, Palermo, Italy | [b] Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

Keywords: Nonlinear differential equation, oscillation and non-oscillation, asymptotic behavior, comparison technique, third-order differential equation

DOI: 10.3233/ASY-211710

Journal: Asymptotic Analysis, vol. 128, no. 4, pp. 445-463, 2022