Corrigendum and addendum to “non-autonomous quasilinear elliptic equations and Ważewski’s principle”

In this addendum we fill a gap in a proof and we correct some results appearing in [12]. In the original paper [12] we classified positive solutions for the following equation ∆pu + K(r)uσ−1 = 0 where r = |x|, x ∈ ℝn, n > p > 1, σ = np/(n − p) and K(r) is a function strictly positive and bounded. In fact [12] had two main purposes. First, to establish asymptotic conditions which are sufficient for the existence of ground states with fast decay and to classify regular and singular solutions: these results are correct but need some non-trivial further explanations. Second to establish some computable conditions on K which are sufficient to obtain multiplicity of ground states with fast decay in a non-perturbation context. Also in this case the original argument contained a flaw: here we correct the assumptions of [12] by performing a new nontrivial construction. A third purpose of this addendum is to generalize results of [12] to a slightly more general equation ∆pu + rδK(r)uσ(δ)−1 = 0 where δ > −p, and σ(δ) = p(n + δ)/(n − p).