On a problem of lower limit in the study of nonresonance with Leray-Lions operator

Abstract

We prove the solvability of the Dirichlet problem $$displaylines{ Au = f(u)+h quadext{in } Omega , cr u = 0 quadext{on }partial Omega }$$ for a given $h$, under a condition involving only the asymptotic behaviour of the potential $F$ of $f$, where $A$ is a Leray-Lions operator.

Keywords

• Leray-Lions operator
• Nonresonance
• fist eigenvalue.