Multiparameter bifurcation and symmetry breaking of solutions of elliptic differential equations

Abstract

In this article, we analyze solutions of the following system of elliptic differential equations \begin{equation*} \begin{cases} - \Delta u = \Lambda u + \nabla_u \eta(u, \Lambda) & \text{ in } \Omega\\ u = 0 & \text{ on } \partial \Omega. \end{cases} \end{equation*} We provide sufficient evidence to prove the existence of global bifurcation points of nontrivial solutions of this system. Moreover, we describe a symmetry breaking phenomenon that occurs on continua of nontrivial solutions of it.