2026-01-022026-01-022025CARVALHO, Marcos L. M.; GASINSKI, Leszek; SANTOS JUNIOR, João R.; SILVA, Edcarlos D. Quasilinear elliptic problems via nonlinear rayleigh quotient. Asymptotic Analysis, Newcastle, v. 145, n. 3, p. 1706-1730, 2025. DOI: 10.1177/09217134251330366. Disponível em: https://journals.sagepub.com/doi/full/10.1177/09217134251330366. Acesso em: 11 dez. 2025.0921-7134e- 1875-8576https://journals.sagepub.com/doi/full/10.1177/09217134251330366It is established existence and multiplicity of solution for the following class of quasilinear elliptic problems:{−ΔΦu = 𝜆a(x)|u|q−2u + |u|p−2u, x ∈ Ω,u = 0, x ∈ 𝜕Ω,where Ω ⊂ ℝN, N ≥ 2, is a smooth bounded domain, 1 < q < 𝓁 ≤ m < p < 𝓁∗ and Φ : ℝ → ℝ is suitable N-function.The main feature here is to show whether the Nehari method can be applied to find the largest positive number 𝜆∗ > 0in such a way that our main problem admits at least two distinct solutions for each 𝜆 ∈ (0, 𝜆∗ ). Furthermore, using somefine estimates and some extra assumptions on Φ, we prove the existence of at least two positive solutions for 𝜆 = 𝜆∗and 𝜆 ∈ (𝜆∗, 𝜆) where 𝜆 > 𝜆∗engAcesso RestritoQuasilinear elliptic problemsConcave–convex nonlinearitiesNonhomogeneous operatorsNehari methodRayleighquotienArtigo10.1177/09217134251330366