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Nonexistence criteria for polyharmonic boundary-value problems
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Monica Lazzo
Published/Copyright:
September 25, 2009
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
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- A uniqueness theorem for meromorphic mappings without counting multiplicities
- On the regularity of H-surfaces with free boundaries on a smooth support manifold
- Schwarz inequality for squares of harmonic conjugate functions
- Two spaces conditions for integrability of the Fourier transform
- An example concerning islands of meromorphic functions and their derivatives
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Keywords for this article
polyharmonic equations;
radial solutions;
Dirichlet boundary conditions;
Navier boundary conditions;
nonexistence of solutions
Articles in the same Issue
- A generalization of a theorem by Křížek, Luca, and Somer on elite primes
- A uniqueness theorem for meromorphic mappings without counting multiplicities
- On the regularity of H-surfaces with free boundaries on a smooth support manifold
- Schwarz inequality for squares of harmonic conjugate functions
- Two spaces conditions for integrability of the Fourier transform
- An example concerning islands of meromorphic functions and their derivatives
- Nonexistence criteria for polyharmonic boundary-value problems
