Pacific Journal of Mathematics

The behavior of solutions of a linear differential equation of second order.

Richard A. Moore

Article information

Source
Pacific J. Math., Volume 5, Number 1 (1955), 125-145.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103044615

Mathematical Reviews number (MathSciNet)
MR0068690

Zentralblatt MATH identifier
0064.08401

Subjects
Primary: 36.0X

Citation

Moore, Richard A. The behavior of solutions of a linear differential equation of second order. Pacific J. Math. 5 (1955), no. 1, 125--145. https://projecteuclid.org/euclid.pjm/1103044615


Export citation

References

  • [1] W. B. Fite, Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19(1918), 341-352.
  • [2] E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234-252.
  • [3] E. L. Ince, Researchesinto the characteristic numbers of the Mathieuequation^ Proc. Roy. Soc. Edinburgh, 46(1925), 20-29.
  • [4] E. L. Ince, The real zeros of solutions of a linear differential equation with periodic coefficients, Proc. London Math. Soc. 25(1926), 53-58.
  • [5] A. Kneser, Untersuchungen uber die reelen Nullstellender Integrate linearer Differentialgleichungen, Math. Ann. 42(1893), 409-435.
  • [6] A. Kneser, Untersuchung und asymptotische Darstellung der Integrate gewisser Differentialgleichungenbei gross en reelen Werthen des Arguments, J. Reine Angew. Math. 116(1896), 178-212.
  • [7] W. Leighton, Bounds for the solutionsof a second order linear differential equa- tion, Proc. Nat. Acad. Sci. 35(1949), 190-191.
  • [8] W. Leighton, Principal quadratic functonalsand self-adjoint second-order dif- ferential equations, Proc. Nat. Acad. Sci. 35(1949), 192-193.
  • [9] W. Leighton, On self-adjoint differential equations of second order, Proc. Nat. Acad. Sci. 35 (1949), 656-657.
  • [10] W. Leighton, The detection of the oscillation of solutions of a second-order linear differential equation, Duke J. Math. 17 (1950), 57-62.
  • [11] M. Morse, and W. Leighton, Singular quadratic functionals,Trans. Amer. Math. Soc. 40(1936), 252-286.
  • [12] A. Wiman, Vber die reelen L'sungen der linearen Differentialgleichungenzweiter rdnung, Ark. Mat. (1917), 22.
  • [13] A. Wintner, On the Laplace-Fouriertranscendents occurring in mathematical physics, Amer. J. Math. 69(1947), 87-98.
  • [14] A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115- 117.