Global secondary bifurcation in a non-linear boundary value problem

We consider a steady-state non-linear boundary value problem which arises i n 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 b ifurcation, it is shown that positive, bounded solutions exist for all phys ically relevant values of a critical parameter. A certain class of these so lutions is discussed with respect to the application to tumour growth. (C) 1999 Academic Press.