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Published in:
2013 | OriginalPaper | Chapter
The Critical Hyperbola for a Hamiltonian Elliptic System with Weights
Authors : Djairo G. de Figueiredo, Ireneo Peral, Julio D. Rossi
Published in: Djairo G. de Figueiredo - Selected Papers
Publisher: Springer International Publishing
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In this paper we look for existence results for nontrivial solutions to the system,
$$ \left\{ {\begin{array}{*{20}c} { - \Updelta u = \frac{{v^{p} }}{{\left| x \right|^{\alpha } }}} & {{\text{in}}\,\Upomega ,} \\ { - \Updelta v = \frac{{u^{p} }}{{\left| x \right|^{\beta } }}} & {{\text{in}}\,\Upomega ,} \\ \end{array} } \right. $$
with Dirichlet boundary conditions,
u
=
v
= 0 on ∂Ω and α, β <
N.
We find the existence of a critical hyperbola in the (
p, q)
plane (depending on α, β and
N
) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking theorem).