On a nonresonance condition between the first and the second eigenvalues for the p-Laplacian

Abstract

We are concerned with the existence of solution for the Dirichlet problem −Δpu=f(x,u)+h(x) in Ω, u=0 on ∂Ω, when f(x,u) lies in some sense between the first and the second eigenvalues of the p-Laplacian Δp. Extensions to more general operators which are (p−1)-homogeneous at infinity are also considered.