Abstract

In this paper, we introduce a new class of quasilinear operators, which represents a nonlocal version of the operator studied by Stuart (Milan J Math 79:327–341, 2011), inspired by models in nonlinear optics. We will study the existence of at least one or two solutions in the cone X := {u ∈ H^s_0: u ≥ 0} using variational methods. For this purpose, we analyze two scenarios: the asymptotic sublinear and linear growth. Additionally, in the sublinear case, we establish a nonexistence result.