Ambrosetti–Prodi problems for the Robin (p, q)-Laplacian. (October 2022) - Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Zhang, Jian
Abstract: The classical Ambrosetti–Prodi problem considers perturbations of the linear Dirichlet Laplace operator by a nonlinear reaction whose derivative jumps over the principal eigenvalue of the operator. In this paper, we develop a related analysis for parametric problems driven by the nonlinear Robin ( p, q ) -Laplace operator (sum of a p -Laplacian and a q -Laplacian). Under hypotheses that cover both the ( p − 1 ) -linear and the ( p − 1 ) -superlinear case, we prove an optimal existence, multiplicity, and non-existence result, which is global in the parameter λ > 0 .