Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space

Nakao Hayashi (), Elena I. Kaikina () and Takayoshi Ogawa ()
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Nakao Hayashi: Tohoku University
Elena I. Kaikina: Centro de Ciencias Matemáticas, UNAM Campus Morelia
Takayoshi Ogawa: Tohoku University

Partial Differential Equations and Applications, 2021, vol. 2, issue 6, 1-24

Abstract: Abstract We consider the inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity in general space dimension $$n\ge 3$$ n ≥ 3 . We present some results on global existence in time and uniquness of small solutions to integral equations associated to the original problem.

Keywords: Nonlinear Schrödinger equation; Large time asymptotics; Inhomogeneous Dirichlet-boundary value problem; Upper half-line; Primary; 35Q35 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00120-9

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