Singular solutions for coercive quasilinear elliptic inequalities with nonlocal terms. (August 2020) - Filippucci, Roberta
Abstract: We study the inequality div ( | x | − α | ∇ u | m − 2 ∇ u ) ≥ ( I β ∗ u p ) u q in B 1 ∖ { 0 } ⊂ R N, where α > 0, N ≥ 1, m > 1, p, q > m − 1 and I β denotes the Riesz potential of order β ∈ ( 0, N ) . We obtain sharp conditions in terms of these parameters for which positive singular solutions exist. We further establish the asymptotic profile of singular solutions to the double inequality a ( I β ∗ u p ) u q ≥ div ( | x | − α | ∇ u | m − 2 ∇ u ) ≥ b ( I β ∗ u p ) u q in B 1 ∖ { 0 } ⊂ R N, where a ≥ b > 0 are constants.