Abstract
The theory of boundary value problems has been applied by Lichtenstein to problems of the calculus of variations. The object of this paper will be to show that some of his results [7] on one-dimensional problems can be carried over to certain types of singular calculus of variations problems. The chief difficulty in extending Lichtenstein's results to singular problems lies in the fact that the associated boundary value problem may be degenerate (that is, in the Grenzkreisfall in Weyl's terminology [9], p. 238) and that the spectrum need not consist of a sequence of eigenvalues tending to infinity, but can contain continuous and cluster spectra. In the sequel, the following terminology will be used: A realvalted function y = y(x), where 0 ? x < oo, will be said to belong to class Q, if (i) y(x) is continuous for 0? x < oo;
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