Let l denote a second order
elliptic expression in divergence form and with coefficients defined in an exterior
domain. In this paper it is shown that, under suitable conditions, the equation
lv = 0 has an a.e. positive generalized solution v defined in a neighborhood of
infinity. This is done under weaker conditions on the coefficients of l than was
previously required. It is then shown that the existence of such a v implies the
finiteness of the negative spectrum of operators naturally associated with
l.