We consider equations involving the truncated Laplacians Pₖ^ and having lower-order terms with singular potentials posed in punctured balls. We study both the principal eigenvalue problem and the problem of classification of solutions, in dependence on their asymptotic behaviour near the origin, for equations having also superlinear absorption lower order terms. In the case of Pₖ^+, owing to the mild degeneracy of the operator, we obtain results which are analogous to the results for the Laplacian in dimension k. On the other hand, for operator Pₖ^-, we show that the strong degeneracy in ellipticity of the operator produces radically different results.
Birindelli et al. (Wed,) studied this question.