Abstract
We obtain estimates on the possible growth or decay rates as λ → 0 of sup |uλ|, where uλ ≢ O satisfies the nonlinear elliptic boundary value problen Luλ = λ f(x,uλ) in a bounded domain subject to homogensous Dirichlet boundary conditions. The estimates generalize existing results by allowing f(x,O) ≠ 0. The analysis is based on integration by parts and Sobolev inequalitie.