Simple zeros of solutions of -order linear differential equations

Author:
W. J. Kim

Journal:
Proc. Amer. Math. Soc. **28** (1971), 557-561

MSC:
Primary 34.42

DOI:
https://doi.org/10.1090/S0002-9939-1971-0274861-5

MathSciNet review:
0274861

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Abstract: Let the th-order linear differential equation have a nontrivial solution with zeros (counting multiplicities) on an interval . A condition under which has a solution with simple zeros on is established.

Also, a new proof is given for a known result concerning an interval of the type .

**[1]**P. Hartman,*Unrestricted -parameter families*, Rend. Circ. Mat. Palermo (2)**7**(1958), 123-142. MR**21**#4211. MR**0105470 (21:4211)****[2]**W. J. Kim,*On the extremal solutions of th-order linear differential equations*(to appear).**[3]**Z. Opial,*On a theorem of O. Aramă*, J. Differential Equations**3**(1967), 88-91. MR**34**#6194. MR**0206375 (34:6194)****[4]**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****[5]**T. L. Sherman,*Properties of solutions of th order linear differential equations*, Pacific J. Math.**15**(1965), 1045-1060. MR**32**#2654. MR**0185185 (32:2654)****[6]**-,*Conjugate points and simple zeros for ordinary differential equations*, Trans. Amer. Math. Soc.**146**(1969), 397-411. MR**0255912 (41:572)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0274861-5

Keywords:
Existence of solutions with simple zeros,
linear equations,
ordinary,
th-order,
real-valued continuous coefficients

Article copyright:
© Copyright 1971
American Mathematical Society