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

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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)

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 ) ) α ′ = p ( t ) y α ( τ ( 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.

Suggested Citation

  • Blanka Baculikova, 2021. "Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments," Mathematics, MDPI, vol. 9(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2552-:d:654075
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    Cited by:

    1. Taher S. Hassan & Qingkai Kong & Bassant M. El-Matary, 2023. "Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order," Mathematics, MDPI, vol. 11(6), pages 1-10, March.

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