BOUNDARY VALUE PROBLEM INVOLVING THE p-LAPLACIAN ON THE SIERPINSKI GASKET

In this paper, we study the following boundary value problem involving the weak p-Laplacian: -Delta(p)u = lambda a(x)|u|(q-1)u + b(x)|u|(l-1)u in S\S-0; u = 0 on S-0, where S is the Sierpinski gasket in R-2, S-0 is its boundary, lambda > 0, p > 1, 0 < q < p - 1 < l and a, b : S -> R are bounded nonnegative functions. We will show the existence of at least two nontrivial weak solutions to the above problem for a certain range of lambda using the analysis of fibering maps on suitable subsets.