Unbounded solutions of the stationary Schrödinger equation on Riemannian manifolds
This paper deals with the investigation of the behaviour of solutions of the stationary Schrödinger equation in relation to the geometry of the manifold in question. More precisely the authors study question of existence of unbounded solutions of \[ Lu:= \Delta u- cu= 0,\tag{1} \] where \(c\) is a smooth nonnegative function on a non-compact Riemannian manifiold \(M\) without boundary and are interested in the interrelation between problems of existence of solutions of (1) and off some compact \(\mathbb B\subset M\) with the same growth ``at infinity''. To this end, the authors use a new approach based on the consideration of equivalence classes of functions on \(M\) (for bounded solutions this approach was known).
scientific article; zbMATH DE number 2112949