Global bifurcation of solutions to elliptic systems with system and domain symmetries
Analysis of PDEs
2025-10-24 v1
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.
Cite
@article{arxiv.2510.20462,
title = {Global bifurcation of solutions to elliptic systems with system and domain symmetries},
author = {Piotr Stefaniak},
journal= {arXiv preprint arXiv:2510.20462},
year = {2025}
}