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Dirichlet problem with indefinite nonlinearities

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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 \(h_ + \ge 0\), g 1(u)u and g 2(u)u are positive for |u| > > 1. Some existence results are given for superlinear g 1 and g 2 via the Morse theory.

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Kung-Ching Chang & Mei-Yue Jiang

Authors
  1. Kung-Ching Chang
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  2. Mei-Yue Jiang
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Additional information

Received: 16 Januray 2003, Accepted: 26 August 2003, Published online: 24 November 2003

Mathematics Subject Classification (2000):

35J20, 35J25, 58E05

Parts of the work were completed while the authors were visiting the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. The authors thank the hospitality of ICTP. Both authors are supported by NSFC, RFDP, MCME, the second author is also supported by the Foundation for University Key Teacher of the Ministry of Education of China and the 973 project of the Ministry of Science and Technology of China.

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Chang, KC., Jiang, MY. Dirichlet problem with indefinite nonlinearities. Cal Var 20, 257–282 (2004). https://doi.org/10.1007/s00526-003-0236-7

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  • DOI: https://doi.org/10.1007/s00526-003-0236-7

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