On the nonlinear Neumann problem with critical and supercritical nonlinearities

The Neumann Problem for Semilinear Elliptic Equations with Critical Sobolev Exponent

“…For the proofs of Lemmas 5.1 and 5.2 we refer to [14] We next establish an inequality which will allow us to control the concentration on ∂Ω of Palais-Smale sequences for J λ . First we introduce some notation analogous to the case with constant coefficients.…”

On the Neumann problem with the Hardy–Sobolev potential

“…Further extension of these results to the case when Q is not constant can be found in [6,7]. The existence results in this case depend on the relationship between the global maximum Q M = max x∈¯ Q(x) and Q m = max x∈∂ Q(x).…”

A nonlinear general Neumann problem involving two critical exponents

“…In [11], the authors were interested to the case p ≡ 1, f (x, u) = 0 and the presence of two critical nonlinearities. They derived some existence results by the use of the concentration compactness principle see [18].…”