Concentration and Multiplicity of Solutions for a Non-Linear Schrödinger Equation with Critical Frequency: N-dimensional Finite Case
We study the finite case of a nonlinear Schrödinger equation (NSE) with critical frequency, considered by Byeon & Wang. Adapting the machinery used by Felmer & Mayorga-Zambrano tu study the flat case, we prove the existence of infinitely pairs of solutions for NSE, not necessarily po...
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| Формат: | bachelorThesis |
| Язык: | eng |
| Опубликовано: |
2020
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| Предметы: | |
| Online-ссылка: | http://repositorio.yachaytech.edu.ec/handle/123456789/252 |
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| Итог: | We study the finite case of a nonlinear Schrödinger equation (NSE) with critical frequency, considered by Byeon & Wang. Adapting the machinery used by Felmer & Mayorga-Zambrano tu study the flat case, we prove the existence of infinitely pairs of solutions for NSE, not necessarily positive, given by the Ljusternik-Schnirelmann category and the properties of the Krasnoselskii genus. These solutions show a concentration phenomena around the zeros of the potential and have an particular asymptotic profile in an appropriate semiclassical limit. |
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