Abstract
We investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in \({\mathbb R}^{N}\), 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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ZL was supported by NSFC Grant Numbers 11901418, 11771319.
YM was supported by JSPS KAKENHI Grant Numbers 19H01797, 19H05599.
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Ghergu, M., Liu, Z., Miyamoto, Y. et al. Nonlinear Inequalities with Double Riesz Potentials. Potential Anal 59, 97–112 (2023). https://doi.org/10.1007/s11118-021-09962-9
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DOI: https://doi.org/10.1007/s11118-021-09962-9