2025-12-302025-12-302026SILVA, Edcarlos D.; CARVALHO, Marcos L. M.; CARDOSO, Márcia S. B. A. Stein-Weiss problems via nonlinear Rayleigh quotient for concave-convex nonlinearities. Journal of Mathematical Analysis and Applications, Amsterdam, v. 553, n. 1, e129828, 2026. DOI: 10.1016/j.jmaa.2025.129828. Disponível em: https://www.sciencedirect.com/science/article/pii/S0022247X25006092. Acesso em: 9 dez. 2025.0022-247Xe- 1096-0813https://www.sciencedirect.com/science/article/pii/S0022247X25006092In the present work, we consider existence and multiplicity of positive solutions for nonlocal elliptic problems driven by the Stein-Weiss problem with concave-convex nonlinearities defined in the whole space . More precisely, we consider the following nonlocal elliptic problem:where . Furthermore, we assume also that  is a bounded potential,  in  and  in  for some specific . We assume also that  and ⁎ where  and ⁎. Our main contribution is to find the largest ⁎ such that our main problem admits at least two positive solutions for each ⁎. In order to do that we apply the nonlinear Rayleigh quotient together with the Nehari method. Moreover, we prove a Brezis-Lieb type Lemma and a regularity result taking into account our setting due to the potentials .engAcesso RestritoStein-Weiss type problemsNonlinear Rayleigh quotientRegularity resultsBrezis-Lieb type identityNehari methodArtigo10.1016/j.jmaa.2025.129828