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Cross-constrained variational problem and the non-linear Klein-Gordon equations. (English) Zbl 1154.35003

In [Commun. Partial Differ. Equations 30, No. 10–12, 1429–1443 (2005; Zbl 1081.35109)], the second author of the paper, developed a type of cross-constrained variational method by means of which sharp threshold of blowup and global existence for the solution of the non-linear Schrödinger equation with harmonic potential have been derived. In the present paper, authors investigate by the same method, the same problem for the non- linear Klein-Gordon equation with an inverse square potential, in three dimensions.

MSC:

35A15 Variational methods applied to PDEs
35L15 Initial value problems for second-order hyperbolic equations

Citations:

Zbl 1081.35109
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References:

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