Journal article 697 views 63 downloads
Nonlinear Inequalities with Double Riesz Potentials
Marius Ghergu,
Zeng Liu,
Yasuhito Miyamoto,
Vitaly Moroz 
Potential Analysis, Volume: 59
Swansea University Author:
Vitaly Moroz
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© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License
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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...
| Published in: | Potential Analysis |
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| ISSN: | 0926-2601 1572-929X |
| Published: |
Springer Science and Business Media LLC
2021
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa58510 |
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| 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 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. |
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| Keywords: |
Nonlinear integral inequalities; Riesz potentials; Nonlocal positivity principle; Liouville theorems |
| College: |
Faculty of Science and Engineering |
| Funders: |
IReL Consortium |