EXISTENCE OF 2 BOUNDARY BLOW-UP SOLUTIONS FOR SEMILINEAR ELLIPTIC-EQUATIONS

In this paper we consider the boundary blow-up problem Delta u = f(u) in Omega, u(x) --> infinity as x --> partial derivative Omega, and its non-autonomous version in a bounded, convex C-2-domain Omega of R-N. We give growth conditions on f at +/- infinity which imply the existen ce of two distinct blowup solutions. The cases, (a) f has a zero, and (b) min f > 0, are fundamentally different. In case (a) we have a posi tive and a sign-changing blow-up solution. In case (b) we introduce a bifurcation parameter lambda into the equation Delta u = lambda f(u) a nd show that for 0 < lambda < lambda(crit) there are blow-up solutions and for lambda > lambda(crit) there is no blow-up solution. (C) 1997 Academic Press.