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Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach

Khalid A. Abdul-Zahra, Zeev Sobol Orcid Logo

Memoirs on Differential Equations and Mathematical Physics, Volume: 96, Pages: 1 - 28

Swansea University Author: Zeev Sobol Orcid Logo

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Abstract

In this work, we study the non-existence of a solution to an eigenvalue problem for the Gross–Pitaevskii equation for Bose–Einstein condensation with repulsive interaction and a trapping potential given as Borel regular measure which vanishes at infinity in some sense. By differential equation appro...

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Published in: Memoirs on Differential Equations and Mathematical Physics
ISSN: 1512-0015
Published: Razmadze Mathematical Institute 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa70550
first_indexed 2025-10-01T07:10:05Z
last_indexed 2026-01-16T05:31:43Z
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spelling 2026-01-15T15:57:54.8260590 v2 70550 2025-10-01 Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach f318e4c186ab19e3d3d3591a2e075d03 0000-0003-4862-427X Zeev Sobol Zeev Sobol true false 2025-10-01 MACS In this work, we study the non-existence of a solution to an eigenvalue problem for the Gross–Pitaevskii equation for Bose–Einstein condensation with repulsive interaction and a trapping potential given as Borel regular measure which vanishes at infinity in some sense. By differential equation approach, we obtain various results on the nonexistence of the eigenvalue problem. Some celebrated Hardy type inequalities are obtained. Journal Article Memoirs on Differential Equations and Mathematical Physics 96 1 28 Razmadze Mathematical Institute 1512-0015 Bose–Einstein condensate, Hardy inequality, killing potential Technique, Pokhozhaev’s test function 31 12 2025 2025-12-31 http://www.jeomj.rmi.ge/memoirs/vol96/contents.htm http://www.jeomj.rmi.ge/memoirs/vol96/contents.htm COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Not Required 2026-01-15T15:57:54.8260590 2025-10-01T02:05:14.5323449 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Khalid A. Abdul-Zahra 1 Zeev Sobol 0000-0003-4862-427X 2
title Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
spellingShingle Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
Zeev Sobol
title_short Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
title_full Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
title_fullStr Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
title_full_unstemmed Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
title_sort Bose–Einstein Condensation and Non-Existence Solution: Differential Equation Approach
author_id_str_mv f318e4c186ab19e3d3d3591a2e075d03
author_id_fullname_str_mv f318e4c186ab19e3d3d3591a2e075d03_***_Zeev Sobol
author Zeev Sobol
author2 Khalid A. Abdul-Zahra
Zeev Sobol
format Journal article
container_title Memoirs on Differential Equations and Mathematical Physics
container_volume 96
container_start_page 1
publishDate 2025
institution Swansea University
issn 1512-0015
publisher Razmadze Mathematical Institute
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://www.jeomj.rmi.ge/memoirs/vol96/contents.htm
document_store_str 0
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description In this work, we study the non-existence of a solution to an eigenvalue problem for the Gross–Pitaevskii equation for Bose–Einstein condensation with repulsive interaction and a trapping potential given as Borel regular measure which vanishes at infinity in some sense. By differential equation approach, we obtain various results on the nonexistence of the eigenvalue problem. Some celebrated Hardy type inequalities are obtained.
published_date 2025-12-31T05:32:57Z
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score 11.096027

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