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

Bégout, Pascal and Diaz, Jesus Ildefonso (2015) Existence of weak solutions to some stationary Schrödinger equations with singular nonlinearity. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 109 (1). pp. 43-63.

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Official URL: http://tse-fr.eu/pub/28121

Abstract

We prove some existence (and sometimes also uniqueness) of weak solutions to some station-
ary equations associated to the complex Schr�odinger 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

Item Type: Article
Language: English
Date: March 2015
Refereed: Yes
Place of Publication: Madrid
Uncontrolled Keywords: Nonlinear Schrödinger equation, Different boundary conditions, Unbounded domains, Non local terms, Data in weighted spaces, Existence, Uniqueness, Smoothness
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 02 May 2018 10:22
Last Modified: 02 May 2018 10:22
OAI ID: oai:tse-fr.eu:28121
URI: http://publications.ut-capitole.fr/id/eprint/25606

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