The $k$th conjugate point function for an even order linear differential equation
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- by George W. Johnson
- Proc. Amer. Math. Soc. 42 (1974), 563-568
- DOI: https://doi.org/10.1090/S0002-9939-1974-0333340-X
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Abstract:
For an even order, two term equation ${L_n}y = p(x)y,p(x) > 0$, x in $[0,\infty )$, the kth conjugate point function ${\eta _k}(a)$ is defined and is shown to be a strictly increasing continuous function with domain [0, b) or $[0,\infty )$. Extremal solutions are defined as nontrivial solutions with $n - 1 + k$ zeros on $[a,{\eta _k}(a)]$, and are shown to have exactly $n - 1 + k$ zeros, with even order zeros at a and ${\eta _k}(a)$ and exactly $k - 1$ odd order zeros in $(a,{\eta _k}(a))$, thus establishing that ${\eta _k}(a) < {\eta _{k + 1}}(a)$.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 563-568
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0333340-X
- MathSciNet review: 0333340