A Robin problem for a class of quasilinear operators and a related minimizing problem

Abstract

In this paper we establish the existence of multiple radial solutions for a class of quasilinear operators with nonlinear boundary Robin conditions. Besides other conditions, we consider the nonlinearities having a behavior at -∞ at least like a linearity of slope less than first eigenvalue λ1(R). The technical approach is by variational methods, which is mainly based on a version of Mountain Pass Theorem due to Ghoussoub and Preiss.