Existence of weak solutions to some stationary Schrödinger equations with singular nonlinearity

We prove some existence (and sometimes also uniqueness) of weak solutions to some stationary equations associated to the complex Schrödinger operator under the presence of a singular nonlinear term. Among other new facts, with respect some previous results in the literature for such type of nonlinea...

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Detalles Bibliográficos
Autores: Begout, Pascal, Díaz Díaz, Jesús Ildefonso
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33890
Acceso en línea:https://hdl.handle.net/20.500.14352/33890
Access Level:acceso abierto
Palabra clave:517.9
Nonlinear Schrödinger equation
Different boundary conditions
Unbounded domains
Non local term
Data in weighted spaces
Existence
Uniqueness
Smoothness
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
Descripción
Sumario:We prove some existence (and sometimes also uniqueness) of weak solutions to some stationary equations associated to the complex Schrödinger operator under the presence of a singular nonlinear term. Among other new facts, with respect some previous results in the literature for such type of nonlinear potential terms, we include the case in which the spatial domain is possibly unbounded (something which is connected with some previous localization results by the authors),the presence of possible non-local terms at the equation, the case of boundary conditions different to the Dirichlet ones and, finally, the proof of the existence of solutions when the right-hand side term of the equation is beyond the usual L2-space.