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Hille-Wintner type comparison theorem for selfadjoint fourth order linear differential equations


Author: L. Erbe
Journal: Proc. Amer. Math. Soc. 80 (1980), 417-422
MSC: Primary 34C10; Secondary 34C11
DOI: https://doi.org/10.1090/S0002-9939-1980-0580996-5
MathSciNet review: 580996
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Abstract: The well-known Hille-Wintner Theorem for second order linear differential equations is extended to fourth order selfadjoint equations.


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  • [1] J. H. Barrett, Oscillation theory of ordinary differential equations, Advances in Math. 3 (1969), 415-509. MR 0257462 (41:2113)
  • [2] G. J. Butler, Hille-Wintner comparison theorems for second order ordinary differential equations, Proc. Amer. Math. Soc. 76 (1979), 51-59. MR 534390 (80h:34039)
  • [3] U. Elias, Nonoscillation and eventual disconjugacy, Proc. Amer. Math. Soc. 66 (1977), 269-275. MR 0460791 (57:784)
  • [4] -, Oscillatory solutions and extremal points for a linear differential equation, Arch. Rational Mech. Anal. 71 (1979), 177-198. MR 525223 (81c:34027)
  • [5] -, Focal points for a linear differential equation whose coefficients are of constant signs, Trans. Amer. Math. Soc. 249 (1979), 187-202. MR 526317 (80h:34041)
  • [6] E. Hille, Nonoscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234-252. MR 0027925 (10:376c)
  • [7] H. C. Howard, Oscillation criteria for fourth order linear differential equations, Trans. Amer. Math. Soc. 96 (1960), 296-311. MR 0117379 (22:8159)
  • [8] K. Kreith, Comparison theorems for a class of selfadjoint fourth order differential equations, Proc. Amer. Math. Soc. 67 (1977), 67-73. MR 0492534 (58:11643)
  • [9] W. Leighton and Z. Nehari, On the oscillation of solutions of selfadjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325-377. MR 0102639 (21:1429)
  • [10] Z. Nehari, Green's functions and disconjugacy, Arch. Rational Mech. Anal. 62 (1976), 53-76. MR 0412519 (54:642)
  • [11] C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968. MR 0463570 (57:3515)
  • [12] C. T. Taam, Nonoscillatory differential equations, Duke Math. J. 19 (1952), 493-497. MR 0051994 (14:557d)
  • [13] A. Wintner, On the comparison theorem of Kneser-Hille, Math. Scand. 5 (1957), 255-260. MR 0096867 (20:3349)
  • [14] J. S. W. Wong, Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients, Trans. Amer. Math. Soc. 144 (1969), 197-215. MR 0251305 (40:4536)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0580996-5
Article copyright: © Copyright 1980 American Mathematical Society

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