Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators

Year 2018, Volume: 1 Issue: 2, 74 - 87, 31.08.2018

Albo Carlos Cavalheiro

Abstract

In this article, we prove the existence and uniqueness of solutions for the Navier problem
(P)



∆

ω(x)(|∆u|
p−2∆u + |∆u|
q−2∆u)

− div
ω(x)(|∇u|
p−2∇u + |∇u|
q−2∇u)

= f(x) − div(G(x)), in Ω,
u(x) = ∆u = 0, in ∂Ω,
where Ω is a bounded open set of R
N (N ≥ 2), f
ω
∈L
p
0
(Ω, ω) and G
ω
∈ [L
q
0
(Ω, ω)]N .

Keywords

Degenerate nonlinear elliptic equations, weighted Sobolev space, 2010 MSC: 35J60, 35J70

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