Acta mathematica scientia, Series B >
ON A CLASS OF INHOMOGENEOUS, ENERGY-CRITICAL, FOCUSING, NONLINEAR SCHRÖDINGER EQUATIONS
Received date: 2012-08-20
Online published: 2013-11-20
Supported by
Supported by NSF of China (11101450, 11071239).
In this paper, we study the Cauchy problem of the inhomogeneous energycritical Schr¨odinger equation: i∂tu = −Δu−k(x)|u| 4/N−2 u, N ≥3. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in the nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, Invent. Math. 166, 645-675 (2006)], where only the radial case is considered in dimensions 3, 4, 5.
Key words： focusing Schr¨odinger equation; critical energy
LIU Zhao-Xia . ON A CLASS OF INHOMOGENEOUS, ENERGY-CRITICAL, FOCUSING, NONLINEAR SCHRÖDINGER EQUATIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(6) : 1522 -1530 . DOI: 10.1016/S0252-9602(13)60101-0
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