Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations

• Autorzy: Naito Manabu

Identyfikatory

DOI

10.7494/OpMath.2023.43.2.221

• Języki publikacji: EN

Abstrakty

EN

We consider the half-linear differential equation (|x′|αsgn x′)′ + q(t)|x|αsgn x = 0, t ≥ t0, under the condition [formula] It is shown that if certain additional conditions are satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t → ∞.

Słowa kluczowe

EN

asymptotic behavior; nonoscillatory solution; half-linear differential equation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 2
• Strony: 221--246
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Naito Manabu

• Ehime University, Faculty of Science, Department of Mathematics, Matsuyama 790-8577, Japan

Bibliografia

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• [6] J. Jaroš, T. Kusano, T. Tanigawa, Nonoscillatory half-linear differential equations and generalized Karamata functions, Nonlinear Anal. 64 (2006), 762–787.
• [7] T. Kusano, J.V. Manojlović, Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations, Electron. J. Qual. Theory Differ. Equ. 2016, Paper no. 62, 24 pp.
• [8] T. Kusano, J.V. Manojlović, Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions, Georgian Math. J. 28 (2021), 611–636.
• [9] J.V. Manojlović, Asymptotic analysis of regularly varying solutions of second-order half-linear differential equations, Kyoto University, RIMS Kokyuroku, 2080 (2018), 4–17.
• [10] M. Naito, Asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations, Arch. Math. (Basel) 116 (2021), 559–570.
• [11] M. Naito, Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I, Opuscula Math. 41 (2021), 71–94.
• [12] M. Naito, Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II, Arch. Math. (Brno) 57 (2021), 41–60.
• [13] P. Řehák, Asymptotic formulae for solutions of half-linear differential equations, Appl. Math. Comput. 292 (2017), 165–177.
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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)