Existence of solutions for discontinuous functional equations and elliptic boundary-value problems.
Let Ω be a bounded domain in Rn with n ≥ 3. In this paper we are concerned with the problem of finding u ∈ H01 (Ω) satisfying the nonlinear elliptic problemsΔu + |u|(n+2/n-2) + f(x) = 0 in Ω and u(x) = 0 on ∂Ω, andΔu + u + |u|(n+2/n-2) + f(x) = 0 in Ω and u(x) = 0 on ∂Ω, when of f ∈ L∞(Ω).
This paper is devoted to the existence of conformal metrics on with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.