Superlinear singular double phase problems
We examine three singular Dirichlet problems driven by the double phase operator. One of the problems is nonparametric and the other two are parametric. In all problems, the perturbation is “superlinear”, but does not satisfy the Ambrosetti-Rabinowitz condition. We prove existence and multiplicity results for the problems. For the parametric problems, the results are global in the parameter $$\lambda >0$$ . Our approach uses variational tools from the critical point theory, truncations and comparisons and critical groups.
Authors
- Nikolaos S. Papageorgiou (ORCID: https://orcid.org/0000-0003-4800-1187)
- Vicenţiu D. Rădulescu (ORCID: https://orcid.org/0000-0003-4615-5537)
- Li Cai
Institutions
- National Technical University of Athens (GR)
- Yulin Normal University (CN)
- University of Agriculture in Krakow (PL)
- Azerbaijan Scientific-Research & Design-Prospecting Power Engineering Institute (AZ)
- Baku Engineering University (AZ)
- Brno University of Technology (CZ)
- AGH University of Krakow (PL)
- Yangzhou University (CN)
Publication Details
- Journal
- Nonlinear Differential Equations and Applications NoDEA
- Published
- 2026-06-27
- DOI
- https://doi.org/10.1007/s00030-026-01238-8
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Natural Science Foundation of Guangxi Zhuang Autonomous Region
- National Natural Science Foundation of China
- Jiangsu University
- Vysoké Učení Technické v Brně
- Natural Science Foundation of Jiangsu Province
- Yangzhou University
- Akademia Górniczo-Hutnicza im. Stanislawa Staszica
- Yulin Normal University
- Bagui Scholars Program of Guangxi Zhuang Autonomous Region