PreprintCC BY 4.0arXiv
Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian
Abstract
We prove global existence of the Cauchy problem of a Schrodinger equation with the logarithmic laplacian and a pure power linearity. We address the focusing and the defocusing cases, and we obtained a sharp blow-up in time result.
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BibTeX
@misc{hajaiej2026powertype,
title = {{Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian}},
author = {Hichem Hajaiej},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39146},
eprint = {2610.39146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39146},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian
AU - Hichem Hajaiej
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39146
UR - https://arxiv.org/abs/2610.39146
AB - We prove global existence of the Cauchy problem of a Schrodinger equation with the logarithmic laplacian and a pure power linearity. We address the focusing and the defocusing cases, and we obtained a sharp blow-up in time result.
ER -