  The eigenvalue problem for the square integrable solutions is studied usually
for elliptic equations. In this note we consider such a problem for the
hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation
could help to answer the question why elementary particles have a discrete mass
spectrum. An infinite family of square integrable solutions for the
Klein-Gordon equation on the Friedman type manifolds is constructed. These
solutions have a discrete mass spectrum and a finite action. In particular the
solutions on de Sitter space are investigated.
