Existence and Asymptotic Behavior for Solutions to Boundary Blow-up Elliptic Problems

This paper deals with the existence of solutions to the elliptic equation Delta u = k(x)f(u) in D satisfying the boundary blow- up condition u vertical bar(partial derivative D) = infinity, where D subset of R-N is an open bounded domain with smooth boundary partial derivative D. Under suitable assumptions on k and f, we show the existence of at least one solution u. Under additional hypotheses on k, we give asymptotic estimate for u near the boundary.