Geodesic
Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials
Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 217-228

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For singularly perturbed Schrödinger equations with decaying potentials at infinity we construct semiclassical states of a critical frequency concentrating on spheres near zeroes of the potentials. The results generalize some recent work of Ambrosetti–Malchiod–Ni [3] which gives solutions concentrating on spheres where the potential is positive. The solutions we obtain exhibit different behaviors from the ones given in [3].
DOI : 10.4171/jems/48
Classification : 35-XX, 00-XX
Keywords: Nonlinear Schrödinger Equations, critical frequency, concentrations on spheres 
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     author = {Jaeyoung Byeon and Zhi-Qiang Wang},
     title = {Spherical semiclassical states of a critical frequency for {Schr\"odinger} equations with decaying potentials},
     journal = {Journal of the European Mathematical Society},
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     volume = {8},
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     year = {2006},
     doi = {10.4171/jems/48},
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Jaeyoung Byeon; Zhi-Qiang Wang. Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials. Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 217-228. doi: 10.4171/jems/48

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