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- Title
Nonlinear Biharmonic Equations with Critical Potential.
- Authors
Hui Xiong; Yao Shen
- Abstract
In this paper, we study two semilinear singular biharmonic equations: one with sub–critical exponent and critical potential, another with sub–critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non–singular cases, and we get an interesting result.
- Subjects
BIHARMONIC equations; PARTIAL differential equations; NUMERICAL analysis; NUMERICAL solutions to biharmonic equations; ASYMPTOTIC theory in partial differential equations; SEPARATION of variables; NUMERICAL solutions to partial differential equations
- Publication
Acta Mathematica Sinica, 2005, Vol 21, Issue 6, p1285
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-004-0502-4