Bifurcation and symmetry breaking of solutions of systems of elliptic differential equations

In this article we study global bifurcations of weak solutions of the following variational system of elliptic differential equations {−Δu=λAu+∇uη(u,λ)in Ωu=0on ∂Ω. We prove sufficient conditions for the existence of unbounded continua of nontrivial solutions emanating from the trivial ones and necessary conditions for the existence of bounded continua. Moreover, we describe a symmetry breaking phenomenon that occurs on that continua.