On a class of spectral problems on the half-line and their applications to multi-dimensional problems

  • Michael Solomyak

    Weizmann Institute of Science, Rehovot, Israel

Abstract

\begin{abstract} A survey of estimates on the number of negative eigenvalues (bound states) of the Sturm--Liouville operator on the half-line, as depending on the properties of the function and the value of the coupling parameter . The central result is Theorem 5.1, giving a sharp sufficient condition for the semi-classical behavior , and the necessary and sufficient conditions for a ``super-classical'' growth rate with any given . Similar results for the problem on the whole are also presented. Applications to the multi-dimensional spectral problems are discussed.

Cite this article

Michael Solomyak, On a class of spectral problems on the half-line and their applications to multi-dimensional problems. J. Spectr. Theory 3 (2013), no. 2, pp. 215–235

DOI 10.4171/JST/43