Non-convergent radial solutions of semilinear elliptic equations

Article type: Research Article

Authors: Maier, Stanislaus

Affiliations: Institut für Mathematik, Universität Augsburg, Universitätsstraße 8, D-86159 Augsburg, Germany

Note: [] The author has been supported by the Deutsche Forschungsgemeinschaft.

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→∞.

DOI: 10.3233/ASY-1994-8403

Journal: Asymptotic Analysis, vol. 8, no. 4, pp. 363-377, 1994