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Infinitely Many Solutions of Nonlinear Elliptic Systems

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

Abstract

In this paper we study elliptic systems of the form
$$ \left\{ {_{\Delta _v = H_{u(x,u,v)in\Omega } }^{ - \Delta _u = H_v (x,u,v)in\Omega } } \right. $$
(1.1)
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
$$ \left\{ {_{\Delta _v + v = H_u (x,u,v)in\mathbb{R}^N }^{ - \Delta _u + u = H_v (x,u,v)in\mathbb{R}^N } } \right. $$
(1.2)

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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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