2025-12-302025-12-302025ASSIS, L. R. S. de; CARVALHO, M. L. M.; SILVA, E. D. da; SALORT, A. Superlinear fractional Φ-Laplacian type problems via the nonlinear Rayleigh quotient with two parameters. Journal of Differential Equations, Amsterdam, v. 445, e113655, 2025. DOI: 10.1016/j.jde.2025.113655. Disponível em: https://www.sciencedirect.com/science/article/pii/S0022039625006825. Acesso em: 9 dez. 2025.0022-0396e- 1090-2732https://www.sciencedirect.com/science/article/pii/S0022039625006825In this work, we establish the existence and multiplicity of weak solutions for nonlocal elliptic problems driven by the fractional Φ-Laplacian operator, in the presence of a sign-indefinite nonlinearity. More specifically, we investigate the following nonlocal elliptic problem:where  and . The exponents p and q are bounded in terms of the fractional Orlicz-Sobolev critical exponent. Here, the potentials  satisfy some suitable hypotheses. Our main objective is to find some positive values for the parameters  and  where the Nehari method can be effectively applied. To achieve this, we apply the nonlinear Rayleigh quotient along with a detailed analysis of the fibering maps associated with the energy functional. Furthermore, we study the asymptotic behavior of the weak solutions to the main problem as  or .engAcesso RestritoFractional Φ-LaplacianDouble parametersSuperlinear nonlinearitiesNehari methodNonlinear Rayleigh quotientArtigo10.1016/j.jde.2025.113655