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Nonlinear Inequalities with Double Riesz Potentials

Marius Ghergu, Zeng Liu, Yasuhito Miyamoto, Vitaly Moroz Orcid Logo

Potential Analysis, Volume: 59

Swansea University Author: Vitaly Moroz Orcid Logo

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DOI (Published version): 10.1007/s11118-021-09962-9

Abstract

We investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in RN, where α, β ∈ (0, N), p, q > 0 and Iα, Iβ denote the Riesz potentials of order α and β respectively. Our approach relies on a nonlocal positivity principle which allows us to derive opti...

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Published in: Potential Analysis
ISSN: 0926-2601 1572-929X
Published: Springer Science and Business Media LLC 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa58510
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first_indexed 2021-10-28T16:19:30Z
last_indexed 2023-01-11T14:39:09Z
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spelling v2 58510 2021-10-28 Nonlinear Inequalities with Double Riesz Potentials 160965ff7131686ab9263d39886c8c1a 0000-0003-3302-8782 Vitaly Moroz Vitaly Moroz true false 2021-10-28 SMA We investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in RN, where α, β ∈ (0, N), p, q > 0 and Iα, Iβ denote the Riesz potentials of order α and β respectively. Our approach relies on a nonlocal positivity principle which allows us to derive optimal ranges for the parameters α, β, p and q to describe the existence and the nonexistence of a solution. The optimal decay at infinity for such solutions is also discussed. Journal Article Potential Analysis 59 Springer Science and Business Media LLC 0926-2601 1572-929X Nonlinear integral inequalities; Riesz potentials; Nonlocal positivity principle; Liouville theorems 26 10 2021 2021-10-26 10.1007/s11118-021-09962-9 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University Other IReL Consortium 2023-06-29T15:13:48.4939287 2021-10-28T17:15:39.8545512 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Marius Ghergu 1 Zeng Liu 2 Yasuhito Miyamoto 3 Vitaly Moroz 0000-0003-3302-8782 4 58510__21361__dae928a40306462f9e69ecd3fd737d1e.pdf Ghergu2021_Article_NonlinearInequalitiesWithDoubl.pdf 2021-10-28T17:18:59.9999693 Output 368587 application/pdf Version of Record true © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License true eng http://creativecommons.org/licenses/by/4.0/
title Nonlinear Inequalities with Double Riesz Potentials
spellingShingle Nonlinear Inequalities with Double Riesz Potentials
Vitaly Moroz
title_short Nonlinear Inequalities with Double Riesz Potentials
title_full Nonlinear Inequalities with Double Riesz Potentials
title_fullStr Nonlinear Inequalities with Double Riesz Potentials
title_full_unstemmed Nonlinear Inequalities with Double Riesz Potentials
title_sort Nonlinear Inequalities with Double Riesz Potentials
author_id_str_mv 160965ff7131686ab9263d39886c8c1a
author_id_fullname_str_mv 160965ff7131686ab9263d39886c8c1a_***_Vitaly Moroz
author Vitaly Moroz
author2 Marius Ghergu
Zeng Liu
Yasuhito Miyamoto
Vitaly Moroz
format Journal article
container_title Potential Analysis
container_volume 59
publishDate 2021
institution Swansea University
issn 0926-2601
1572-929X
doi_str_mv 10.1007/s11118-021-09962-9
publisher Springer Science and Business Media LLC
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
document_store_str 1
active_str 0
description We investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in RN, where α, β ∈ (0, N), p, q > 0 and Iα, Iβ denote the Riesz potentials of order α and β respectively. Our approach relies on a nonlocal positivity principle which allows us to derive optimal ranges for the parameters α, β, p and q to describe the existence and the nonexistence of a solution. The optimal decay at infinity for such solutions is also discussed.
published_date 2021-10-26T15:13:44Z
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score 10.998093

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