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

GAN, ZAIHUI ; ZHANG, JIAN

Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 467-481

Résumé

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.

Détail

DOI : 10.1017/S0017089508004345

Mots-clés : 35A15, 35L15

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