ABSTRACT
It is easy to give examples of interesting Simple VL-regions, and in the concluding section of this paper, we shall discuss two of them. The whole point of introducing the concept of Simple VL-regions is that both a weighted continuous and a weighted compact imbedding theorem holds for these regions (see [Sh, p. 15 and p. 46]). Using these imbedding theorems, we shall establish multiplicity results for a weighted (i.e., singular) elliptic operator. Also, Simple VL-regions need not be bounded or have finite volume, unlike the situation which prevails for most of the previous multiplicity results in the literature (see[Am], [He], and [Ra, p.54]).
