On a problem of lower limit in the study of nonresonance

Abstract

We prove the solvability of the Dirichlet problem {−Δpu=f(u)+h in Ω, u=0 on ∂Ω for every given h, under a condition involving only the asymptotic behaviour of the potential F of f with respect to the first eigenvalue of the p-Laplacian Δp. More general operators are also considered.

Keywords

• p-Laplacian
• nonresonance
• first eigenvalue.