On positive solutions of minimal growth for singular p-Laplacian with potential term

Let Omega be a domain in R-d, d >= 2, and 1 < p < infinity. Fix V is an element of L-loc(infinity)(Omega) Consider the functional Q and its Gdteaux derivative Q(') given by Q(u):=1/p integral(Omega)(|del u|(p)+V|u|(p))dx, Q'(u):=-del. (|del u|(p-2)del u) + V|u|(p-2)u. It is assumed that Q >= 0 on C-0(infinity)(Omega). In a previous paper [221 we discussed relations between the absence of weak coercivity of the functional Q on C-0(infinity) (Omega) and the existence of a generalized ground state. In the present paper we study further relationships between functional-analytic properties of the functional Q and properties of positive solutions of the equation Q'(u) = 0.