Abstract
We study the pointwise asymptotic behavior of the radially symmetric ground state solution of a quasilinear elliptic equation involving the m-Laplacian in ℝn with two competing parameters. Roughly speaking, the first parameter ε measures the distance to a critical growth problem while the second parameter δ measures the weight of the “linear” term. We obtain the exact asymptotic behavior of the ground state, for any 1<m<n, both at the origin and outside the origin, when the equation tends to critical growth (ε→0). We also obtain the “equilibrium relation” between ε and δ so that when they both vanish according to this relation, ground states neither blow up nor vanish. The results of this paper complete the description begun in [F. Gazzola, J. Serrin, Ann. Inst. H. Poincaré AN 19 (2002) 477–504].
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