Global secondary bifurcation in a non-linear boundary value problem

We consider a steady-state non-linear boundary value problem which arises in modelling the formation of vascular networks in response to tumour growth. Global bifurcation from both trivial and non-trivial solution branches is considered, with emphasis on the latter. By investigating such secondary bifurcation, it is shown that positive, bounded solutions exist for all physically relevant values of a critical parameter. A certain class of these solutions is discussed with respect to the application to tumour growth.