Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in Rd for d = 3,4

Abstract We consider a system of coupled elliptic partial differential equations with critical growth in R d for d = 3 , 4 and study bifurcations of three families of radially symmetric, bounded solutions. We reduce the problems of the three families to those of three symmetric homoclinic orbits in a four-dimensional reversible system of ordinary differential equations and show that transcritical or pitchfork bifurcations of the three families occur at infinitely many parameter values. Numerical computations are also given to demonstrate our theoretical results.