Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I

• Autorzy: Naito Manabu

Identyfikatory

DOI

10.7494/OpMath.2021.41.1.71

• Języki publikacji: EN

Abstrakty

EN

We consider the half-linear differential equation of the form [formula], under the assumption [formula]. It is shown that if a certain condition is 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; Hardy-type inequality

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 1
• Strony: 71--94
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Naito Manabu

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

Bibliografia

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• [6] J. Jaros, T. Kusano, T. Tanigawa, Nonoscil lation theory for second order half-linear differential equations in the framework of regular variation, Results Math. 43 (2003), 129-149.
• [7] J. Jaros, T. Kusano, T. Tanigawa, Nonoscil latory half-linear differential equations and generalized Karamata functions, Nonlinear Anal. 64 (2006), 762-787.
• [8] 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.
• [9] T. Kusano, J.V. Manojlović, Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions, Georgian Math. J., to appear.
• [10] V. Marić, Regular Variation and Differential Equations, Lecture Notes in Mathematics, vol. 1726, Springer, Berlin, Heidelberg, New York, 2000.
• [11] M. Naito, Asymptotic behavior of nonoscil latory solutions of half-linear ordinary differential equations, Arch. Math. (Basel), to appear.
• [12] P. Rehak, 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 MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).