Ambrosetti–Prodi problems for the Robin (p, q)-Laplacian. (October 2022)

• Record Type: Journal Article
• Authors: Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Zhang, Jian
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Ambrosetti–Prodi problem -- (p, q)-Laplace operator -- One-sided superlinear perturbation -- One-sided sublinear perturbation -- Nonlinear regularity theory -- Nonlinear maximum and anti-maximum principles; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103640
• Languages: English
• ISSNs: 1468-1218

Abstract

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 .