We employ a version of the Picone Identity, suitable for the pLaplacean, to obtain a Sturm Comparison Theorem for generalized solutions. This answers a question posed by Dunninger in 1995. INTRODUCTION The establishment of a Picone Identity has recently proved useful as a simple means of establishing a variety of results in Spectral Theory, Sturm Comparison Theorems, etc. for the p-Laplacean, -AP, and related equations. To the best of our knowledge, this version of the identity was first established by Dunninger [5], and exploited by Allegretto and Huang [3], [4], where several other references are given. More recent related arguments may be found in [2], [6], and [7]. In general terms, the results in the above references extend to -AP results that had long been known for the ordinary Laplacean, i.e. for p = 2. It is the purpose of this paper to continue in this direction. The main motivation for this work is an open question mentioned in [5], and related to earlier results given in [1]. Specifically, we first recall that a typical conclusion of a Sturm Theorem is that a solution v of a differential equation (or inequality) cannot be positive in a domain Q. Employing Maximum Principle arguments, one then shows that v must actually change sign in Q. The continuity of v is important in these arguments. In [1], it was shown for p = 2 and v solution of an equation, that even if v is merely assumed to be in H1'2, then one could still conclude that ,u(xjv(x) > 0) > 0 and ,u(xjv(x) 0. That such a conclusion may hold for -AP is mentioned in [5] as an open question, which we answer. Furthermore, we investigate the set {xlv = 0} and show that while this set may have positive measure (under the degeneracy condition we give), it is possible to locate this set to some extent and to obtain conditions such that it has measure zero and thus obtain the conclusion ,u(xjv(x) 0, ,u(xjv(x) > 0) > 0. These latter results thus also represent a modest extension of the linear result given in [1]. Received by the editors March 2, 2000. 2000 Mathematics Subject Classification. Primary 35B05; Secondary 35D99.