Entire nodal solutions with prescribed symmetry to Caffarelli-Kohn-Nirenberg equations
Abstract
We establish the existence of sign-changing entire solutions to weighted critical $ p $-Laplace equations of the Caffarelli-Kohn-Nirenberg type. In doing so, we investigate classes of symmetry and show that, for suitable symmetry configurations, there exists a non-trivial solution which changes sign and respects the corresponding prescribed symmetry. In addition, we describe conditions under which these symmetry-types are incompatible. Especially, we demonstrate the existence of entire nodal solutions for an infinite number of distinct symmetry-types.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Solidification and crystal growth phenomena
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 58
- Issue
- 0
- Pages
- 390–416
- Publication date
- 17 August 2026