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CROSS-CONSTRAINED VARIATIONAL PROBLEM AND THE NON-LINEAR KLEIN–GORDON EQUATIONS*

Published online by Cambridge University Press:  01 September 2008

ZAIHUI GAN  and
JIAN ZHANG
ZAIHUI GAN
Affiliation:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P.R. China e-mail: ganzaihui2008cn@yahoo.com.cn
JIAN ZHANG
Affiliation:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P.R. China e-mail: ganzaihui2008cn@yahoo.com.cn
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Abstract

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In this paper, we put forward a cross-constrained variational method to study the non-linear Klein–Gordon equations with an inverse square potential in three space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish some new types of invariant sets for the equation and derive a sharp threshold of blowup and global existence for its solution. Finally, we give an answer to the question how small the initial data are for the global solution to exist.

Keywords

35A1535L15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 467 - 481
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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