On a class of nonhomogeneous equations of Hénon-type : symmetry breaking and non radial solutions.
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Date
2017
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Abstract
In this work we study the following Hénon-type equation
⎧⎪⎨
⎪⎩
−div
(
|∇u|p−2∇u
|x|ap
)
= |x|βf(u), in B;
u > 0, in B;
u = 0, on ∂B;
where B :=
{
x ∈ RN ; |x| < 1
}
is a ball centered at the origin, the parameters
verify the inequalities 0 ≤ a < N−p
p , N ≥ 4, β > 0, 2 ≤ p < Np+pβ
N−p(a+1) , and the
nonlinearity f is nonhomogeneous. By minimization on the Nehari manifold, we
prove that for large values of the parameter β there is a symmetry breaking and
non radial solutions appear.
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Keywords
Degenerate operator
Citation
ASSUNÇÃO, R. B. et al. On a class of nonhomogeneous equations of Hénon-type : symmetry breaking and non radial solutions. Nonlinear Analysis, v. 165, p. 102-120, dez. 2017. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0362546X17302420>. Acesso em: 16 jun. 2018.