Existence of two boundary blow-up solutions for semilinear elliptic equations

[摘要] 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 existence 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 positive and a sign-changing blow-up solution. In case (b) we introduce a bifurcation parameter lambda into the equation Delta u = lambda f(u) and 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.

[发布日期] 1997-12-10