Superlinear singular double phase problems
Abstract
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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Nonlinear Differential Equations and Applications NoDEA
- Publisher
- Springer Science and Business Media LLC
- Volume
- 33
- Issue
- 4
- Publication date
- 27 June 2026
- Language
- EN