Abstract
We study solutions u=u(t) of an initial value problem for u″+(n−1)/t u′+f(u)=0, which have the additional property that the limit of u as t approaches infinity does not exist. Besides some examples, we give necessary conditions on the non-linearity f for the existence of such (non-convergent) solutions. One corollary of these investigations will be that, if f(u)u>0 for small |u|≠0 then every solution u(·;p) (with |p| small enough) of the initial value problem (1.1), stated below, converges to zero as t→∞.
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