Concentration and multiplicity of solutions for a non-linear Schrödinger equation with critical frequency: infinite case

In this work we prove existence, multiplicity, concentration phenomena and decay of solutions for the nonlinear Schrödinger equation. Using the properties of the Krasnoselskii genus and by a Ljusternik-Schnirelman scheme we prove the existence of an infinite number of solutions vk,ε, wk for (Pε) and (P) while presenting concentration results about the solutions of (Pε). We prove the subconvergence, up to scaling of vk,ε to a solution of (P) and exponential decay of solutions away from Ω. Our results are congruent with the ones obtained by Byeon & Wang (2002), Felmer & Mayorga (2007) and Mayorga, Medina & Muñoz (2020) in each of their respective studies of the Critical Frequency cases.

• Huvudupphovsman: Aguas Barreno, Ariel Alejandro (author)
• Materialtyp: bachelorThesis
• Språk: eng
• Publicerad: 2021
• Ämnen: Ecuación de Schrödinger No-lineal; Caso infinito; Frecuencia crítica; Multiplicidad; Concentración; Nonlinear Schrödinger equation; Infinite case; Critical frequency; Multiplicity; Concentration
• Länkar: http://repositorio.yachaytech.edu.ec/handle/123456789/415