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On one oscillatory criterion for the second order linear ordinary differential equations

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Języki publikacji
EN
Abstrakty
EN
The Riccati equation method is used to establish an oscillatory criterion for second order linear ordinary differential equations. An oscillatory condition is obtained for the generalized Hill's equation. By means of examples the obtained result is compared with some known oscillatory criteria.
Rocznik
Strony
589--601
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Institute of Mathematics NAS of Armenia 0019 Erevan, str. M. Bagramian 24/5, Armenia
Bibliografia
  • [1] H.Kh. Abdullah, A note on the oscillation of second order differential equations, Czechoslovak Mathematical Journal 54 (2004) 4, 949-954.
  • [2] J. Deng, Oscillation criteria for second order linear differential equations, J. Math. Anal. Appl. 271 (2002), 283-287.
  • [3] O. Dosly, E. Jansova, J. Colas, Eighty fifth anniversary of birthday and scientific legacy of Professor Milos Rab, Arch. Math., 50 (2014), 1-19.
  • [4] A. Elbert, Oscillation/nonoscillation criteria for linear second order differential equations, J. Math. Anal. Appl. 226 (1998), 207-219.
  • [5] G.A. Grigorian, Some properties of solutions of second-order linear ordinary differential equations, Trudy IMM YrO RAN 19 (2003) 1, 69-80.
  • [6] G.A. Grigorian, Properties of solutions of Riccati equation, Journal of Contemporary Mathematical Analysis 42 (2007) 4, 184-197.
  • [7] Ph. Hartman, Ordinary Differential Equations, SIAM, Classics in Applied Mathematics 38, Philadelphia 2002.
  • [8] LV. Kamenev, Integral criterion for oscillation of linear differential equations of second order, Math. Zametki 23 (1978), 249-261.
  • [9] Q. Kong, Interval criteria for oscillation of second-order linear ordinary differential equations, J. Math. Anal. Appl. 229 (1999), 258-270.
  • [10] Q. Kong, M. Pasic, Second Order Differential Equations: Some Significant Results Due to James S. W. Wong, Differential Equations and Applications 6 (2014) 1, 99-163.
  • [11] M.K. Kwong, Integral criteria for second-order linear oscillation, Electron. J. Qual. Theory Differ. Equ. 2006, no. 10, 1-18.
  • [12] M.K. Kwong, J.S.W. Wong, On the oscillation of Hill's Equations under periodic forcing, J. Math. Anal. Appl. 320 (2006), 37-55.
  • [13] M.K. Kwong, M. Pasic, J.S.W. Wong, Rectifiable oscillation in second order linear differential equations, J. Differential Equations 245 (2008), 2333-2351.
  • [14] W.-L. Liu, H.-J. Li, Oscillation criteria for second order linear differential equations with damping, Journal of Applied Analysis 2 (1986) 1, 105-118.
  • [15] J.G. Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a second order-linear differential equations, Computers and Mathematics with Applications 48 (2004), 1693-1699.
  • [16] C.A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York and London, 1968.
  • [17] J. Yan, Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98 (1986), 276-282.
  • [18] Z. Zheng, Note on Wong's paper, J. Math. Anal. Appl. 274 (2002), 466-473.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a87f7b1a-40d1-4a99-8cb5-896e5325bd83
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