On Superquadratic Elliptic Systems

Djairo G. de Figueiredo () and Patricio L. Felmer ()
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Djairo G. de Figueiredo: IMECC-UNICAMP
Patricio L. Felmer: Universidad de Chile, Departamento De Ingeníerfa Matemática, F.C.F.M

A chapter in Djairo G. de Figueiredo - Selected Papers, 1994, pp 387-404 from Springer

Abstract: Abstract 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.

Date: 1994
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DOI: 10.1007/978-3-319-02856-9_26

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