Work

Superlinear singular double phase problems

Year: 2026

Type: article

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.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-026-01238-8

Authors: Li Cai, Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu