Systems-conjugate and focal points of fourth order nonselfadjoint differential equations

Cheng, Sui Sun

doi:10.1090/S0002-9947-1976-0473334-3

Systems-conjugate and focal points of fourth order nonselfadjoint differential equations

Author: Sui Sun Cheng
Journal: Trans. Amer. Math. Soc. 223 (1976), 155-165
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9947-1976-0473334-3
MathSciNet review: 0473334
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Abstract: Systems-conjugate points have been studied by John Barrett in relation to selfadjoint fourth order differential equations of the form $({p_2}u'')'' + {p_0}u = 0$ . This paper extends his results to the general nonselfadjoint fourth order differential equation via a system of second order equations.

[1] William M. Whyburn, On Self-Adjoint Ordinary Differential Equations of the Fourth Order, Amer. J. Math. 52 (1930), no. 1, 171–196. MR 1506751, https://doi.org/10.2307/2370655
[2] Kurt Kreith, A nonselfadjoint dynamical system, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), 77–87. MR 342768, https://doi.org/10.1017/S0013091500015406
[3] John H. Barrett, Systems-disconjugacy of a fourth-order differential equations, Proc. Amer. Math. Soc. 12 (1961), 205–213. MR 130443, https://doi.org/10.1090/S0002-9939-1961-0130443-0
[4] G. A. Bliss and I. J. Schoenberg, On Separation, Comparison and Oscillation Theorems for Self-Adjoint Systems of Linear Second Order Differential Equations, Amer. J. Math. 53 (1931), no. 4, 781–800. MR 1506854, https://doi.org/10.2307/2371226
[5] Philip Hartman and Aurel Wintner, On disconjugate differential systems, Canadian J. Math. 8 (1956), 72–81. MR 74595, https://doi.org/10.4153/CJM-1956-012-4
[6] Walter Leighton and Zeev Nehari, On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325–377. MR 102639, https://doi.org/10.1090/S0002-9947-1958-0102639-X
[7] Walter Leighton, Some elementary Sturm theory, J. Differential Equations 4 (1968), 187–193. MR 224907, https://doi.org/10.1016/0022-0396(68)90035-1