We consider the Cauchy-problem for the parabolic equation [ u_t = Delta u+ f(u,|x|), ] where $x in mathbb R^n$, $n >2$, and $f(u,|x|)$ is either critical or supercritical with respect to the Joseph-Lundgren exponent. In particular, we improve and generalize some known results concerning stability and weak asymptotic stability of positive ground states.
On the non-autonomous hopf bifurcation problem: Systems with rapidly varying coefficients / Franca, M.; Johnson, R.. - In: ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS. - ISSN 1417-3875. - ELETTRONICO. - 2019:56(2019), pp. 1-24. [10.14232/ejqtde.2019.1.56]