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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 28, Issue 4


Nonexistence criteria for polyharmonic boundary-value problems

Monica Lazzo / Paul G. Schmidt
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/anly.2008.0928


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

About the article

* Correspondence address: Universitá di Bari, Dipartimento di Matematica, via Orabona 4, 70125 Bari, Italien,

Published Online: 2009-09-25

Published in Print: 2008-12-01

Citation Information: Analysis International mathematical journal of analysis and its applications, Volume 28, Issue 4, Pages 449–460, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1524/anly.2008.0928.

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