Perturbation of structures of radial solutions to elliptic equations

Abstract

The change of structures of radial solutions to elliptic equations is discussed. Especially, by some perturbation on a "potential function", the non-existence of rapidly decaying solutions fails and the existence of that one is ensured. Also, in another case, the uniqueness of rapidly decaying solutions breaks and multiple rapidly decaying ones appear. Some insights to the number of solutions are also presented.