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arXiv · 0902.0722

Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials

Vitaly Moroz·Jean Van Schaftingen
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Abstract

We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove that if V has a positive local minimum, and if the exponent of the nonlinearity satisfies N/(N-2)<p<(N+2)/(N-2), then for small epsilon the problem admits positive solutions which concentrate as epsilon goes to 0 around the local minimum point of V. The novelty is that no restriction is imposed on the rate of decay of V. In particular, we cover the case where V is compactly supported.

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Vitaly Moroz, Jean Van Schaftingen. 2009-02-04. Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials. https://doi.org/10.1007/s00526-009-0249-y

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