Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space-Reference-Cited by-同舟云学术

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

Published:2021-10-07 Issue:6 Volume:2 Page:
ISSN:2662-2963
Container-title:Partial Differential Equations and Applications
language:en
Short-container-title:Partial Differ. Equ. Appl.

Author:

Hayashi Nakao^ORCID,Kaikina Elena I.,Ogawa Takayoshi

Abstract

AbstractWe 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.

Funder

japan society for the promotion of science

conacyt

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s42985-021-00120-9.pdf

Reference33 articles.

1. Audiard, C.: On the non-homogeneous boundary value problem for Schödingier equations. Discrete Contin. Dyn. Syst. 33, 3861–3884 (2013)

2. Audiard, C.: On the boundary value problem for the Schrödinger equation: compatibility conditions and global existence. Anal. PDE 8, 1113–1143 (2015)

3. Audiard, C.: Global Strichartz estimates for the Schrödinger equation with non zero boundary conditions and applications. Ann. Inst. Fourier (Grenoble) 69(1), 31–80 (2019)

4. Bona, J.L., Sun, S.-M., Zhang, B.-Y.: Nonhomogeneous boundary-value problems for one dimensional nonlinear Schrödinger equations. J. Math. Pures Appl. 9(109), 1–66 (2018)

5. Brezis, H., Gallouet, T.: Nonlinear Schrödinger evolution equation. Nonlinear Anal. 4, 677–681 (1980)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Ginzburg–Landau equation with fractional Laplacian on a upper- right quarter plane;Nonlinearity;2024-05-24

2. Local well‐posedness of the higher‐order nonlinear Schrödinger equation on the half‐line: Single‐boundary condition case;Studies in Applied Mathematics;2023-09-11

3. Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space;Partial Differential Equations and Applications;2021-10-07