Existence of a ground state solution for an elliptic problem with critical growth in an exterior domain
- M. Montenegro, R. Abreu
- Nonlinear Anal
In this article, we study the semilinear elliptic equation −∆u = |u|p(x)−2u, x ∈ R u ∈ D(R ), where N ≥ 3, p(x) = ( p, x ∈ Ω 2∗, x 6∈ Ω, with 2 < p < 2∗ := 2N/(N − 2), Ω ⊂ RN is a bounded set with nonempty interior. By using the Nehari manifold, we obtain a positive ground state solution.