Dirichlet problem with indefinite nonlinearities

  • Kung-Ching Chang
  • Mei-Yue Jiang
Article

Abstract.

We consider the following nonlinear elliptic equation \( -\triangle u -\lambda u = h_-(x) g_1(u) + h_ + (x) g_2(u) \) in a bounded domain \(\Omega\) with the Dirichlet boundary condition, \(h_-\le 0\) and \(h_ + \ge 0\), g1(u)u and g2(u)u are positive for |u| > > 1. Some existence results are given for superlinear g1 and g2 via the Morse theory.

Keywords:

Dirichlet problem Critical groups Indefinite nonlinearities 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • Kung-Ching Chang
    • 1
  • Mei-Yue Jiang
    • 1
  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingChina

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