Boundary singularities of positive solutions of some nonlinear elliptic equations

Abstract

We study the behavior near x0 of any positive solution of (E) −Δu=uq in Ω which vanishes on ∂Ω∖{x0}, where Ω⊂RN is a smooth domain, q⩾(N+1)/(N−1) and x0∈∂Ω. Our results are based upon a priori estimates of solutions of (E) and existence, non-existence and uniqueness results for solutions of some nonlinear elliptic equations on the upper-half unit sphere.