A SINGULAR BOUNDARY VALUE PROBLEM FOR A RIGHT DISFOCAL LINEAR DIFFERENTIAL OPERATOR

Paul W. Eloe, Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316, Paul.Eloe@notes.udayton.edu.

Eric R. Kaufmann, Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, Arkansas 72204-1099, erkaufmann@ualr.edu.

Dynamic Systems and Applications, 5 (1996), No. 2, 175-182.

ABSTRACT: Let n > 2 be an integer and let k Î {1, …, n - 1}. Define the nth order linear differential operator,

L y = y (n) + k - 1
å
l = 0 		al(x) y (l).
We assume that L is right disfocal on [0, ¥) and impose sign conditions on the coefficients, al, l = 0, …, k - 1. We shall then characterize and determine sign properties for limiting Green's functions for the singular boundary value problem,
L y = 0, 0 < x, y(i)(0) = 0, i = 0, …, k - 1. Under further assumptions, we shall obtain a uniquely determined limiting Green's function.

AMS (MOS) subject classification 34B05, 34B27.

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