The th conjugate point function for an even order linear differential equation

Author:
George W. Johnson

Journal:
Proc. Amer. Math. Soc. **42** (1974), 563-568

MSC:
Primary 34C10

MathSciNet review:
0333340

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Abstract: For an even order, two term equation , *x* in , the *k*th conjugate point function is defined and is shown to be a strictly increasing continuous function with domain [0, *b*) or . Extremal solutions are defined as nontrivial solutions with zeros on , and are shown to have exactly zeros, with even order zeros at *a* and and exactly odd order zeros in , thus establishing that .

**[1]**John H. Barrett,*Oscillation theory of ordinary linear differential equations*, Advances in Math.**3**(1969), 415–509. MR**0257462****[2]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[3]**G. W. Johnson,*The zeros of solutions of an even order quasi differential equation*, J. Analyse Math. (to appear).**[4]**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**0102639**, 10.1090/S0002-9947-1958-0102639-X**[5]**A. Ju. Levin,*Some questions on the oscillation of solutions of linear differential equations*, Dokl. Akad. Nauk SSSR**148**(1963), 512–515 (Russian). MR**0146450****[6]**Zeev Nehari,*Disconjugate linear differential operators*, Trans. Amer. Math. Soc.**129**(1967), 500–516. MR**0219781**, 10.1090/S0002-9947-1967-0219781-0

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0333340-X

Keywords:
Extremal solution,
conjugate point,
zero of multiplicity *k*

Article copyright:
© Copyright 1974
American Mathematical Society