Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments

Blanka Baculikova
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Blanka Baculikova: Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia

Mathematics, 2021, vol. 9, issue 20, 1-12

Abstract: In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form r ( t ) ( y ? ( t ) ) ? ? = p ( t ) y ? ( ? ( t ) ) . Such differential equation may possesses two types of nonoscillatory solutions either from the class N 0 (positive decreasing solutions) or N 2 (positive increasing solutions). We establish new criteria for N 0 = ? and N 2 = ? provided that delayed and advanced parts of deviating argument are large enough. As a consequence of these results, we provide new oscillatory criteria. The presented results essentially improve existing ones even for a linear case of considered equations.

Keywords: second order differential equations; delay; advanced; mixed argument; monotonic properties; oscillation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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