### 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 $\lambda \to \infty$.

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 $\lambda \to \infty$.

#### Keywords

Large positive solutions; flat core; sweeping out results

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