Geodesic
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 31-38.

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Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.
DOI : 10.5817/AM2023-1-31
Classification : 34B15, 34B18, 35Q55
Keywords: nonlinear Schrödinger equation; stationary solutions; supercritical dimensions; shooting method 
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     title = {Stationary solutions of semilinear {Schr\"odinger} equations with trapping potentials in supercritical dimensions},
     journal = {Archivum mathematicum},
     pages = {31--38},
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     volume = {59},
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     doi = {10.5817/AM2023-1-31},
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     zbl = {07675572},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-31/}
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Ficek, Filip. Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 31-38. doi : 10.5817/AM2023-1-31. http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-31/

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