Structure of large positive solutions of some semilinear elliptic problems where the nonlinearity changes sign

Abstract

Existence and uniqueness of large positive solutions
are obtained for some semilinear elliptic Dirichlet problems
in bounded smooth domains $\Omega$ with a large parameter $\lambda$.
It is shown that the large positive solution has flat core. The
distance of its flat core to the boundary $\partial \Omega$ is
exactly measured as $\lambda \to \infty$.