Oscillation properties of the disconjugate fourth order selfadjoint differential equation

Author:
Leo J. Schneider

Journal:
Proc. Amer. Math. Soc. **28** (1971), 545-550

MSC:
Primary 34.42

DOI:
https://doi.org/10.1090/S0002-9939-1971-0281999-5

MathSciNet review:
0281999

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Abstract: This paper contains a proof that either all, or none, of the nontrivial solutions of the fourth order linear selfadjoint differential equation have an infinite number of zeros on a half line, provided that no nontrivial solution has more than one double zero on that half line.

**[1]**W. Leighton and Z. 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**21**#1429. MR**0102639 (21:1429)****[2]**M. Morse,*Introduction to analysis in the large*, 2nd ed., Lectures, Institute for Advanced Study, Princeton, N.J., 1951; reprint, 1957. MR**16**, 837. MR**0068140 (16:837c)****[3]**G. Pólya,*On the mean-value theorem corresponding to a given linear homogeneous differential equation*, Trans. Amer. Math. Soc.**24**(1922), 312-324. MR**1501228****[4]**A. Peterson,*The distribution of zeros of extremal solutions of a fourth order differential equation for the -th conjugate point*, J. Differential Equations**8**(1970), 502-511. MR**0269928 (42:4821)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0281999-5

Keywords:
Conjugate point,
disconjugacy,
disconjugacy for ,
Morse index,
nonoscillatory solution,
oscillatory solution,
separation of zeros,
self-adjoint differential equation of fourth order

Article copyright:
© Copyright 1971
American Mathematical Society