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Published in:
2013 | OriginalPaper | Chapter
On Superquadratic Elliptic Systems
Authors : Djairo G. de Figueiredo, Patricio L. Felmer
Published in: Djairo G. de Figueiredo - Selected Papers
Publisher: Springer International Publishing
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In this article we study the existence of solutions for the elliptic system
$$ - \Updelta u = \frac{\partial H}{\partial v}\left( {u,v,x} \right)\,{\text{in}}\Upomega , $$
$$ - \Updelta v = \frac{\partial H}{\partial v}\left( {u,v,x} \right)\,{\text{in}}\Upomega , $$
$$ u = 0,v = 0\,{\text{on}}\,\partial \Upomega $$
where
$$ \Upomega $$
is a bounded open subset of
$$ {\mathbb{R}}^{N} $$
with smooth boundary
$$ \partial \Upomega $$
and the function
H
:
$$ {\mathbb{R}}^{2} \times \overline{\Upomega } \to {\mathbb{R}} $$
, is of class
C
1
.