Multiple solutions for Δγ-Laplace problems without the Ambrosetti–Rabinowitz condition

Abstract

In this paper, we study the existence of multiple solutions for the boundary value problem [Formula: see text] where [Formula: see text] is a bounded domain with smooth boundary in [Formula: see text], nonlinearity [Formula: see text] is subcritical growth and does not satisfy the Ambrosetti–Rabinowitz (AR) condition and [Formula: see text] is the subelliptic operator of the type [Formula: see text] We use variational methods (Mountain pass theorem and Ekeland variational principle).