Existence of a positive solution for a class of non-local elliptic problem with critical growth in Rn.

Nenhuma Miniatura disponível
Data
2022
Título da Revista
ISSN da Revista
Título de Volume
Editor
Resumo
In 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.
Descrição
Palavras-chave
Non-local elliptic equation, Critical exponent, Variational method
Citação
LEME, 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.