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λ(n)-Parameter Families

Published online by Cambridge University Press:  20 November 2018

Ronald M. Mathsen
Ronald M. Mathsen*
Affiliation:
University of Alberta, Edmonton
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I is an interval of R, the set of real numbers, n is a positive integer and F ⊂ Cj (I) for j ≥ 0 large enough so that the following definitions are possible:

(i) Let λ(n) = (λ1, λ2,…,λk) where k, λ1, λ2,…, λk, are positive integers and λ1 + λ2 +… +λk = n. Then λ(n) is an ordered partition of n. The set of all such partitions of n is denoted by P(n).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 185 - 191
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Hartman, P., Unrestricted n-parameter families. Rend. Circ. Mat. Palermo (2) (1959) 123–142.Google Scholar
2. Mathsen, R.M., A disconjugacy condition for y"' + a2" + a1y' + a0y = 0. Proc. Amer. Math. Soc. 17. (1966) 627–632.Google Scholar
3. Mathsen, R.M., Subfunctions for third order ordinary differential equations. (Ph.D. Thesis, University of Nebraska, Lincoln, 1965.)Google Scholar
4. Opial, Z., On a theorem of O. Arama. J. Differential Eqs. 3 (1967) 88–91.Google Scholar
5. Tornheim, L., On n-parameter families of functions and associated convex functions. Trans. Amer. Math. Soc. 69 (1950) 457–467.Google Scholar
6. Levin, A. Ju., Some problems bearing on the oscillation of solutions of linear differential equations. Soviet Math. Dakl. 4 (1963) 121–124.Google Scholar
7. Sherman, T. L., Properties of solutions of Nth order linear differential equations. Pacific J. Math. 15 (3) (1965) 1045–1060.Google Scholar