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 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.

• Главный автор: Muñoz Moncayo, Carlos Andrés (author)
• Формат: bachelorThesis
• Язык: eng
• Опубликовано: 2020
• Предметы: Nonlinear Shcrödinger equation; Critical frequency; Finite case; Multiplicity; Existence; Concentration.; Ecuación de Schrödinger no-lineal; Frecuencia crítica; Caso finito; Multiplicidad; Existencia; Concentración
• Online-ссылка: http://repositorio.yachaytech.edu.ec/handle/123456789/252