Nodal solutions of a p-Laplacian equation

We prove that the p-Laplacian problem −Δp u = f(x, u), with u ∈ u ∈ W 0 1 , p ( Ω ) on a bounded domain Ω ⊂ RN, with p > 1 arbitrary, has a nodal solution provided that f : Ω × R → R is subcritical, and f(x, t) / ∣t∣p − 2 is superlinear. Infinitely many nodal solutions are obtained if, in addition, f(x, −t) = −f(x, t). 2000 Mathematics Subject Classification 35J20, 35J65, 58E05.