Imaginary poles of radial potentials. (English) Zbl 0641.35052

Strauss, Walter A.; Majda, George; Wei, Musheng

Mat. Apl. Comput. 6, 17-24 (1987).

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

Keywords:

scattering frequencies; growing and decaying modes; spherically symmetric potential; compact support; non-negative