Robin double-phase problems with singular and superlinear terms. (April 2021)

• Record Type: Journal Article
• Authors: Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.
• Is Part Of: Nonlinear analysis. Volume 58(2021)
• Publication Date: 2021-04
• Subjects: Nonhomogeneous differential operator -- Nonlinear regularity theory -- Truncation -- Strong comparison principle -- Positive solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103217
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a nonlinear Robin problem driven by the sum of p -Laplacian and q -Laplacian (i.e. the ( p, q ) -equation). In the reaction there are competing effects of a singular term and a parametric perturbation λ f ( z, x ), which is Carathéodory and ( p − 1 ) -superlinear at x ∈ R, without satisfying the Ambrosetti–Rabinowitz condition. Using variational tools, together with truncation and comparison techniques, we prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter λ > 0 varies.