We obtain estimates on the possible growth or decay rates as λ → 0 of sup |u λ |, where u λ ≠ 0 satisfies the nonlinear elliptic boundary value problem lu λ = λ f(x,u λ) in a bounded domain subject to homogeneous Dirichlet boundary conditions. The estimates generalize existing results by allowing f(x,0)≠ 0. The analysis is based on integration by parts and Sobolev inequalities.
ASJC Scopus subject areas
- Applied Mathematics