Nonlinear Inequalities with Double Riesz Potentials
Keyword(s):
AbstractWe investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in ${\mathbb R}^{N}$ 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.
2014 ◽
Vol 1008-1009
◽
pp. 1517-1520
1988 ◽
Vol 11
(1)
◽
pp. 115-119
2012 ◽
Vol 3
(2)
◽
pp. 305-307
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