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Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials

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Abstract

In this paper, we study the Lyapunov stabilities of some “semiclassical” bound states of the (nonhomogeneous) nonlinear Schrödinger equation,

We prove that among those bound states, those which are “concentrated” near local minima (respectively maxima) of the potentialV are stable (respectively unstable). We also prove that those bound states are positive if

is sufficiently small.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, 94720, Berkeley, CA, USA

    Yong-Geun Oh

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  1. Yong-Geun Oh
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Communicated by B. Simon

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Oh, YG. Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials. Commun.Math. Phys. 121, 11–33 (1989). https://doi.org/10.1007/BF01218621

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  • DOI: https://doi.org/10.1007/BF01218621

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