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

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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 →∞.
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Strony
71--94
Opis fizyczny
Bibliogr. 13 poz.
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autor
  • Ehime University Faculty of Science Department of Mathematics Matsuyama 790-8577, Japan
Bibliografia
  • [1] P.R. Beesack, Hardy’s inequality and its extensions, Pacific J. Math. 11 (1961), 39-61.
  • [2] O. Dosly, P. Rehak, Half-Linear Differential Equations, North-Holland Mathematics Studies, vol. 202, Elsevier, Amsterdam, 2005.
  • [3] G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1952.
  • [4] P. Hartman, Ordinary Differential Equations, Classics in Applied Mathematics, vol. 38, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002 (reprinted from original John Wiley & Sons, 1964).
  • [5] J. Jaros, T. Kusano, Self-adjoint differential equations and generalized Karamata functions, Bull. T. CXXIX de Acad. Serbe Sci. et Arts, Classe Sci. Mat. Nat. Sci. Math. 29 (2004), 25-60.
  • [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.
  • [13] P. Rehak, V. Taddei, Solutions of half-linear differential equations in the classes gamma and pi, Differential Integral Equations 29 (2016), 683-714.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
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Bibliografia
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bwmeta1.element.baztech-53d29d67-224c-47be-a741-aa51e8bc3501
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