Existence and multiplicity results for an elliptic problem involving cylindrical weights and a homogeneous term μ.
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Date
2019
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Abstract
We 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.
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Keywords
Supercritical, Degenerate operator, Variational methods
Citation
ASSUNÇÃO, 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.