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Nonlinear Inequalities with Double Riesz Potentials / Marius Ghergu, Zeng Liu, Yasuhito Miyamoto, Vitaly Moroz

Potential Analysis

Swansea University Author: Vitaly Moroz

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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 opti...

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Published in: Potential Analysis
ISSN: 0926-2601 1572-929X
Published: Springer Science and Business Media LLC 2021
Online Access: Check full text

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.
Keywords: Nonlinear integral inequalities; Riesz potentials; Nonlocal positivity principle; Liouville theorems
College: College of Science
Funders: IReL Consortium