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On the number of solutions of right-definite problems with a convergent Dirichlet integral

  • M. S. P. Eastham (a1)

Synopsis

A recently developed asymptotic theory of higher-order differential equations is applied to problems of right-definite type to determine the numbers M+, M of linearly independent solutions with a convergent Dirichlet integral, M+ and M referring to the usual upper and lower λ.-half-planes. Particular attention is given to the phenomenon noted by Karlsson in which one of M+ and M is maximal but not the other. Conditions are given under which M+ (say) is maximal and M is the same, one less, and two less.

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