GENERICITY OF HYPERBOLICITY AND SADDLE-NODE BIFURCATIONS IN REACTION-DIFFUSION EQUATIONS DEPENDING ON A PARAMETER

Semilinear elliptic equations of the form [GRAPHICS] are considered, w here lambda is an element of R is a parameter, Omega subset of R(n) is a bounded domain and f is a smooth non-linear function. It is shown t hat for 'generic' functions f, the set of non-trivial solutions (lambd a,u) consists of a finite, or countable, collection of smooth, 1-dimen sional curves and any such solution is either hyperbolic or is a saddl e-node bifurcation point of the curve.