Disconjugacy and integral inequalities

Clausing, Achim

doi:10.1090/S0002-9947-1980-0570791-X

Disconjugacy and integral inequalities
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by Achim Clausing PDF

Trans. Amer. Math. Soc. 260 (1980), 293-307 Request permission

Abstract:

The basic data in this paper are a disconjugate differential operator and an associated two-point boundary value problem. These define in a natural way a cone of functions satisfying a differential inequality with respect to the operator. By using a result of P. W. Bates and G. B. Gustafson on the monotonicity properties of Green’s kernels it is shown that such a cone has a compact convex base which is a Bauer simplex. This result is used to derive a variety of integral inequalities which include known inequalities of Frank and Pick, Levin and Steckin, Karlin and Ziegler, as well as several new ones.

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