Linking and multiplicity results for the p-Laplacian on unbounded cylinders

We consider the p-Laplacian problem -Delta (p)u = lambdaa(x)/u/(p-2)u + f(x,u) in Ohm, u is an element of W-0(1,p)(Ohm), on unbounded cylinders Ohm = <(<Ohm>)over tilde> x RN-m subset of R-N, N - m greater than or equal to 2, where Delta (p)u = div(/delu/(p-2)delu), lambda is a constant in a certain range, and a is an element of L-N/p(Ohm) boolean AND L-infinity(Ohm) is nonnegative, a not equal 0. Using the principle of symmetric criticality, existence and multiplicity are proved under suitable conditions on a and f. (C) 2001 Academic Press.