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Some stability conditions for a nonlinear differential equation


Author: Don Hinton
Journal: Trans. Amer. Math. Soc. 139 (1969), 349-358
MSC: Primary 34.51
DOI: https://doi.org/10.1090/S0002-9947-1969-0241767-2
MathSciNet review: 0241767
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  • [1] V. A. Ambartsumyan, Theoretical astrophysics, Pergamon Press, New York, 1958.
  • [2] Richard Bellman, Stability theory of differential equations, McGraw-Hill, New York, 1953. MR 0061235 (15:794b)
  • [3] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 0069338 (16:1022b)
  • [4] J. S. W. Wong, Some stability conditions for $ x'' + a(t){x^{2n - 1}} = 0$, SIAM J. Appl. Math. 15 (1967), 889-892. MR 0221042 (36:4094)
  • [5] D. B. Hinton, Some stability conditions for $ y'' + qy = 0$, J. Math. Anal. Appl. 21 (1968), 126-131. MR 0227519 (37:3103)
  • [6] Zeev Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428-445. MR 0087816 (19:415a)
  • [7] F. V. Atkinson, On second-order non-linear oscillations, Pacific J. Math. 5 (1955), 643-647. MR 0072316 (17:264e)
  • [8] Imrick Licko and Marko Švec, Le charactere oscillatione des solutions de l'equation $ {y^{(n)}} + f(x){y^\alpha } = 0,n > 1$, Czecholovak Math. J. (88) 13 (1963), 481-491. MR 0161001 (28:4210)
  • [9] Jaroslav Kurzweil, A note on oscillatory solutions of the equation $ y'' + f(x){y^{2n - 1}} = 0$, Časopis Pěst. Mat. 85 (1960), 357-358. MR 0126025 (23:A3322)
  • [10] J. W. Heidel, The existence of oscillatory solutions for a nonlinear odd order differential equation, (submitted to J. Math. Anal. Appl.).
  • [11] I. T. Kiguradze, On the asymptotic properties of solutions of the equation $ u'' + a(t){u^n} = 0$, Soobšč. Akad. Nauk Gruzin. SSR 30 (1963), 129-136. MR 0150385 (27:386)

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DOI: https://doi.org/10.1090/S0002-9947-1969-0241767-2
Article copyright: © Copyright 1969 American Mathematical Society

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