On a Sobolev critical problem for the superposition of a local and nonlocal operator with the “wrong sign”
Abstract
Abstract We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. The main novelty is that we consider a mixed operator of the form , namely we suppose that the fractional Laplacian has the “wrong sign” and can be seen as a nonlocal perturbation of the purely local case, which is needed to produce a nontrivial solution of the critical problem.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 9
- Publication date
- 20 August 2026
- Language
- EN