Asymptotic properties of ground states of scalar field equations with a vanishing parameter
Asymptotic properties of ground states of scalar field equations with a vanishing parameter
We study the leading order behaviour of positive solutions of the equation -\Delta u +\epsilon u-|u|^{p-2}u+|u|^{q-2}u=0,\qquad x\in\mathbb R^N, where N\ge 3 , q>p>2 and when \epsilon >0 is a small parameter. We give a complete characterization of all possible asymptotic regimes as a function of p , q and N …