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ISSN 1088-6850(e) ISSN 0002-9947(p)

Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities

Author(s): Didier Smets
Journal: Trans. Amer. Math. Soc. 357 (2005), 2909-2938.
MSC (2000): Primary 35J10, 35J70, 58J37
Posted: December 29, 2004
MathSciNet review: 2139932
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Abstract: We study a time-independent nonlinear Schrödinger equation with an attractive inverse square potential and a nonautonomous nonlinearity whose power is the critical Sobolev exponent. The problem shares a strong resemblance with the prescribed scalar curvature problem on the standard sphere. Particular attention is paid to the blow-up possibilities, i.e. the critical points at infinity of the corresponding variational problem. Due to the strong singularity in the potential, some new phenomenon appear. A complete existence result is obtained in dimension 4 using a detailed analysis of the gradient flow lines.

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