Leme, Leandro Correia PaesRodrigues, Bruno Mendes2023-02-072023-02-072022LEME, L. C. P.; RODRIGUES, B. M. Existence of a positive solution for a class of non-local elliptic problem with critical growth in Rn. Mediterranean Journal of Mathematics, v. 19, n. 67, 2022. Disponível em: <https://link.springer.com/article/10.1007/s00009-022-02012-7>. Acesso em: 06 jul. 2022.1660-5454http://www.repositorio.ufop.br/jspui/handle/123456789/16134In this article, we consider the following non-local elliptic equation with critical growth ⎧⎪⎨⎪⎩− a + b RN |∇u| 2 dx p−1 2 Δu = λk(x)uq + u2∗−1, x ∈ RN , u ∈ D1,2(RN ), where N ≥ 3, λ > 0, 2∗:= 2N N−2 , 1 < p ≤ q < 2∗ − 1, a ≥ 0, b ≥ 0 and k(x) ∈ L 2∗ 2∗−q−1 (RN ) is a nonnegative function. Using variational methods and concentration-compactness principle, we obtain a positive solution.en-USrestritoNon-local elliptic equationCritical exponentVariational methodArtigo publicado em periodicohttps://link.springer.com/article/10.1007/s00009-022-02012-7https://doi.org/10.1007/s00009-022-02012-7