Remark on asymptotic behaviors of solutions to a quasi-linear elliptic Dirichlet problem with large diffusion

We study asymptotic behaviors of nontrivial solutions to the Dirichlet problem of a quasi-linear elliptic equation and obtain a lower bound for growth of L∞L∞-norm of the solutions, which implies the L∞L∞-norm of the solutions goes to infinity as the diffusion coefficient goes to infinity.