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Analysis

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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2196-6753
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Volume 28, Issue 4

Issues

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

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

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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[1]
Tingzhi Cheng, Wenxiong Chen, Congming Li, and Lizhi Zhang
Discrete and Continuous Dynamical Systems, 2015, Volume 36, Number 3, Page 1721
[2]
M. Lazzo and P.G. Schmidt
Journal of Differential Equations, 2009, Volume 247, Number 5, Page 1479

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