Global bifurcation of solutions to elliptic systems with system and domain symmetries
Abstract
We study parameterized elliptic systems on symmetric domains with additional system symmetries. We prove the existence of continua of nontrivial solutions bifurcating from the constant branch determined by a critical point of the potential, without assuming nondegeneracy, via the degree for equivariant gradient maps. Our assumptions are formulated in terms of the right-hand side. When the domain is a compact symmetric space, the bifurcating solutions break symmetry at every nonzero level. Under additional assumptions on the right-hand side, the continua are unbounded.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Communications in Partial Differential Equations
- Publisher
- Informa UK Limited
- Volume
- 51
- Issue
- 4
- Pages
- 453–472
- Publication date
- 3 April 2026
- Language
- EN