Multiple solutions for a singular elliptic problem involving Hardy terms on unbounded domains. (Q2343869)

Motivated by a paper of \textit{R. Filippucci} et al. [Commun. Partial Differ. Equations 33, No. 4, 706--717 (2008; Zbl 1147.35038)], the author proves a series of multiplicity results for solutions of quasi-linear elliptic problems on possibly unbounded domains. The equations considered present singular weights and Hardy terms and the strategies adopted are variational. The author points out that in the recent paper [Abstr. Appl. Anal. 2012, Article ID 806397, 15 p. (2012; Zbl 1261.35068)] by \textit{Z. Xiu}, Step 2 of the proof of Lemma 2.7 is not correct and also the argument of Section 3 to show that \(c_m>-\infty \) is not valid, since the energy functional associated to the underlying problem is not bounded below. In the paper under review, the author proves multiplicity results via arguments different from those of the cited paper of Xiu and actually considers a more general setting. Since the problem treated in the paper is singular and the domain \(\Omega \) is possibly unbounded, the loss of compactness of the Sobolev embedding makes the variational techniques more delicate to handle. The paper will be for sure of interest for the readers of the journal Differential and Integral Equations.