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?H0s(?):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. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.