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Title: Linearization technique for oscillation of perturbed half-linear differential equations (English)
Author: Naito, Manabu
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 61
Issue: 1
Year: 2025
Pages: 43-59
Summary lang: English
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Category: math
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Summary: It is shown that oscillation of perturbed second order half-linear differential equations can be derived from oscillation of second order linear differential equations associated with modified Riccati equations. In the main result of the present paper, some of technical assumptions in the known results of this type are removed. (English)
Keyword: half-linear differential equation
Keyword: oscillation
Keyword: modified Riccati equation
MSC: 34C10
DOI: 10.5817/AM2025-1-43
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Date available: 2025-03-24T13:09:56Z
Last updated: 2025-03-24
Stable URL: http://hdl.handle.net/10338.dmlcz/152918
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Reference: [1] Došlá, Z., Došlý, O.: Principal solution of half-linear differential equation: limit and integral characterization.Electron. J. Qual. Theory Differ. Equ. 2008 (2008), 14 pp., paper No. 7. MR 2509168
Reference: [2] Došlý, O.: Perturbations of the half-linear Euler–Weber type differential equation.J. Math. Anal. Appl. 323 (2006), 426–440. MR 2262216, 10.1016/j.jmaa.2005.10.051
Reference: [3] Došlý, O.: Half-linear Euler differential equation and its perturbations.Electron. J. Qual. Theory Differ. Equ. 2016 (2016), 14 pp., paper No. 10. MR 3631082, 10.14232/ejqtde.2016.8.10
Reference: [4] Došlý, O., Elbert, Á.: Integral characterization of the principal solution of half-linear second order differential equations.Studia Sci. Math. Hungar. 36 (2000), 455–469. MR 1798750
Reference: [5] Došlý, O., Fišnarová, S.: Half-linear oscillation criteria: Perturbation in term involving derivative.Nonlinear Anal. 73 (2010), 3756–3766. Zbl 1207.34041, MR 2728552, 10.1016/j.na.2010.07.049
Reference: [6] Došlý, O., Fišnarová, S.: Two-parametric conditionally oscillatory half-linear differential equations.Abstr. Appl. Anal. 2011 (2011), 16 pp., Article ID 182827. MR 2771241, 10.1155/2011/182827
Reference: [7] Došlý, O., Lomtatidze, A.: Oscillation and nonoscillation criteria for half-linear second order differential equations.Hiroshima Math. J. 36 (2006), 203–219. MR 2259737, 10.32917/hmj/1166642300
Reference: [8] Došlý, O., Řehák, P.: Half-Linear Differential Equations.North-Holland Mathematics Studies, vol. 202, Elsevier, Amsterdam, 2005. MR 2158903
Reference: [9] Došlý, O., Řezníčková, J.: Regular half-linear second order differential equations.Arch. Math. (Brno) 39 (2003), 233–245. MR 2010724
Reference: [10] Dosoudilová, M., Lomtatidze, A., Šremr, J.: Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations.Nonlinear Anal. 120 (2015), 57–75. Zbl 1336.34053, MR 3348046
Reference: [11] Elbert, Á., Schneider, A.: Perturbations of the half-linear Euler differential equation.Results Math. 37 (2000), 56–83. Zbl 0958.34029, MR 1742294, 10.1007/BF03322512
Reference: [12] Luey, S., Usami, H.: Asymptotic forms of solutions of half-linear ordinary differential equations with integrable perturbations.Hiroshima Math. J. 53 (2023), 171–189. MR 4612154, 10.32917/h2022005
Reference: [13] Naito, M.: Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I.Opuscula Math. 41 (2021), 71–94. MR 4302442, 10.7494/OpMath.2021.41.1.71
Reference: [14] Naito, M.: Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations.Opuscula Math. 43 (2023), 221–246. MR 4567780, 10.7494/OpMath.2023.43.2.221
Reference: [15] Naito, M.: Oscillation and nonoscillation for two-dimensional nonlinear systems of ordinary differential equations.Taiwanese J. Math. 27 (2023), 291–319. MR 4563521, 10.11650/tjm/221001
Reference: [16] Naito, M.: Oscillation criteria for perturbed half-linear differential equations.Electron. J. Qual. Theory Differ. Equ. 2024 (2024), 18 pp., paper No. 38. MR 4782772
Reference: [17] Naito, M., Usami, H.: On the existence and asymptotic behavior of solutions of half-linear ordinary differential equations.J. Differential Equations 318 (2022), 359–383. MR 4387287, 10.1016/j.jde.2022.02.025
Reference: [18] Řehák, P.: Nonlinear Poincaré–Perron theorem.Appl. Math. Lett. 121 (2021), 7 pp., Article ID 107425. MR 4268643
Reference: [19] Řehák, P.: Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes.Electron. J. Qual. Theory Differ. Equ. 2023 (2023), 28 pp., paper No. 1. MR 4541736
Reference: [20] Zlámal, M.: Oscillation criterions.Časopis Pěst. Mat. Fys. 75 (1950), 213–218. MR 0042578
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