Abstract
We study the asymptotic behaviour of positive groundstate solutions to the quasilinear elliptic equation
- Delta(p)u + epsilon u(p-1) - u(q-1) + u(l-1) = 0 in R-N (P-epsilon)
where 1 < p < N, p < q < l < + infinity and epsilon > 0 is a small parameter. For epsilon -> 0, we give a characterization of asymptotic regimes as a function of the parameters q, l and N. In particular, we show that the behaviour of the groundstates is sensitive to whether q is less than, equal to, or greater than the critical Sobolev exponent p* := pN/N-p.