Assunção, Ronaldo BrasileiroMiyagaki, Olimpio HiroshiLeme, Leandro Correia PaesRodrigues, Bruno Mendes2023-02-072023-02-072019ASSUNÇÃO, R. B. et al. Existence and multiplicity results for an elliptic problem involving cylindrical weights and a homogeneous term μ. Mediterranean Journal of Mathematics, v. 16, n. 33, 2019. Disponível em: <https://link.springer.com/article/10.1007/s00009-019-1317-y>. Acesso em: 06 jul. 2022.1660-5454http://www.repositorio.ufop.br/jspui/handle/123456789/16133We consider the following elliptic problem ⎧⎨ ⎩ − div |∇u| p−2 ∇u |y| ap = μ |u| p−2 u |y| p(a+1) + h(x) |u| q−2 u |y| bq + f(x, u) in Ω, u = 0 on ∂Ω, in an unbounded cylindrical domain Ω := {(y, z) ∈ Rm+1 × RN−m−1 ; 0 <A< |y| <B< ∞}, where A, B ∈ R+, p > 1, 1 ≤ m<N − p, q := N p N − p(a + 1 − b), 0 ≤ μ < μ := m + 1 − p(a + 1) p p , h ∈ L N q (Ω) ∩ L∞(Ω) is a positive function and f : Ω × R → R is a Carath ́eodory function with growth at infinity. Using the Krasnoselski’s genus and applying Z2 version of the Mountain Pass Theorem, we prove, under certain assumptions about f, that the above problem has infinite invariant solutions.en-USrestritoSupercriticalDegenerate operatorVariational methodsArtigo publicado em periodicohttps://link.springer.com/article/10.1007/s00009-019-1317-yhttps://doi.org/10.1007/s00009-019-1317-y