Multigrid Methods for a Semilinear Pde in the Theory of Pseudoplastic Fluids

have been extensively studied. Various existence and uniqueness results are given in [1], [2], and [3], to name a few. More recently, in [4], it is shown that by certain transformations the boundary layer equations for the class of non-Newtonian uids named pseudoplastic can be generalized in the above form for the ODE case n = 1. Under this physical interpretation the above equation, considered in the context of partial di erential equations (n > 1), has been the subject of much study. The equation has a unique classical solution with a bounded domain , where p(x) is a su ciently regular function which is positive on [5]. There exist entire solutions with 2 (0; 1) for p(x) su ciently regular ([6], [7]). This is generalized to all > 0 via the upper and lower solution method ([8]) or other methods ([9]).