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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Green's function of an $ n$-point boundary value problem


Authors: K. M. Das and A. S. Vatsala
Journal: Trans. Amer. Math. Soc. 182 (1973), 469-480
MSC: Primary 34B10
MathSciNet review: 0333324
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Abstract: The Green's function $ {g_n}(x,s)$ for an n-point boundary value problem, $ {y^{(n)}}(x) = 0,y({a_1}) = y({a_2}) = \cdots = y({a_n}) = 0$ is explicitly given. As a tool for discussing $ \operatorname{sgn} g_n(x,s)$ on the square $ [{a_1},{a_n}] \times [{a_1},{a_n}]$, some results about polynomials with coefficients as symmetric functions of a's are obtained. It is shown that

$\displaystyle \int_{{a_1}}^{{a_n}} {\vert{g_n}(x,s)\vert ds} $

is a suitable polynomial in x. Applications to n-point boundary value problems and lower bounds for $ {a_m}\;(m \geq n)$ are included.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0333324-5
PII: S 0002-9947(1973)0333324-5
Keywords: Green's function, multipoint boundary value problem, zeros of solutions
Article copyright: © Copyright 1973 American Mathematical Society