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Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity

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Abstract

In this paper, Fucik spectrum, ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity, and some new results on the existence of nontrivial solutions, multiple solutions and sign-changing solutions are obtained. In one case seven nontrivial solutions are got. The techniques have independent interest.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Shujie Li & Zhitao Zhang

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  1. Shujie Li
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  2. Zhitao Zhang
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Correspondence to Shujie Li or Zhitao Zhang.

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Li, S., Zhang, Z. Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity. Sci. China Ser. A-Math. 44, 856–866 (2001). https://doi.org/10.1007/BF02880135

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  • DOI: https://doi.org/10.1007/BF02880135

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