2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120694The 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.8 pagesGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryMathematical PhysicsDifferential Geometrytext