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Abstract
We discuss some known results and open problems pertaining to the nonexistence of nontrivial solutions for semilinear polyharmonic equations under Dirichlet or Navier boundary conditions. Precise control of the boundary terms in a Pohozaev-type identity allows us to establish a sharp nonexistence criterion for radially symmetric solutions, which closes a gap in the literature.
Keywords: polyharmonic equations; radial solutions; Dirichlet boundary conditions; Navier boundary conditions; nonexistence of solutions
Published Online: 2009-09-25
Published in Print: 2008-12
© by Oldenbourg Wissenschaftsverlag, München, Germany
