Non-existence results for semilinear cooperative elliptic systems via moving spheres

Academic Article


  • Based upon a new development of the method of moving spheres, we introduce a new and general approach for non-existence of positive solutions of cooperative semilinear elliptic systems with the Laplacian as principal part. For supercritical nonlinearities we prove non-existence on bounded star-shaped domains. For subcritical nonlinearities we obtain non-existence results on a class of unbounded domains, which includes e.g. the entire space, certain curved halfspaces and the complement of bounded star-shaped domains. As a by-product we also get a symmetry result on halfspaces. © 2000 Academic Press.
  • Authors

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    Digital Object Identifier (doi)

    Author List

  • Reichel W; Zou H
  • Start Page

  • 219
  • End Page

  • 243
  • Volume

  • 161
  • Issue

  • 1