×

zbMATH — the first resource for mathematics

Imaginary poles of radial potentials. (English) Zbl 0641.35052
Let q(r) be a spherically symmetric potential of compact support in three dimensions. There exists a (growing or decaying) mode of the form exp(kt)p(r) with k real if q(r) is non-positive but no such a solution exists if q(r) is non-negative.

MSC:
35P25 Scattering theory for PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
PDF BibTeX XML Cite