Abstract

We study a multiplicity result for the perturbed p-Laplacian equation −Δpu−λg(x)|u|p−2u=f(x,u)+h(x) in ℝN, where 1<p<N and λ is near λ 1, the principal eigenvalue of the weighted eigenvalue problem −Δpu=λg(x)|u|p−2u in ℝN. Depending on which side λ is from λ 1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.