Infinitely Many Solutions of Nonlinear Elliptic Systems

  • Thomas Bartsch
  • Djairo G. de Figueiredo
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 35)


In this paper we study elliptic systems of the form
$$ \left\{ {_{\Delta _v = H_{u(x,u,v)in\Omega } }^{ - \Delta _u = H_v (x,u,v)in\Omega } } \right. $$
where Ω ⊂ ℝ N , N > 3, is a smooth bounded domain and H: Ω ℝ ℝ → ℝ C 1-function. We shall also consider the case when Ω = ℝ N and in this case the system takes the form
$$ \left\{ {_{\Delta _v + v = H_u (x,u,v)in\mathbb{R}^N }^{ - \Delta _u + u = H_v (x,u,v)in\mathbb{R}^N } } \right. $$


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Copyright information

© Springer Basel AG 1999

Authors and Affiliations

  • Thomas Bartsch
    • 1
  • Djairo G. de Figueiredo
    • 2
  1. 1.Mathematisches InstitutUniversität GiessenGiessenGermany
  2. 2.IMECC, UNICAMPCampinasBrazil

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