Structure of large positive solutions of a class of quasilinear elliptic Dirichlet problems Original Research Article

Existence and uniqueness of large positive solutions are obtained for a class of quasilinear elliptic Dirichlet problems in bounded smooth domains Ω with a large parameter λ. It is shown that a flat core of the large positive solution exists and its existence depends upon the smoothness of the nonlinearity. The distance between the flat core and ∂Ω is precisely measured as λ→∞.