TY - JOUR
T1 - Asymptotic decay of solutions for sublinear fractional Choquard equations
AU - Gallo, Marco
PY - 2024
Y1 - 2024
N2 - Goal of this paper is to study the asymptotic behaviour of the solutions of the following doubly nonlocal equation (−Δ)su+μu=(Iα∗F(u))f(u)onRNwhere s∈(0,1), N≥2, α∈(0,N), μ>0, Iα denotes the Riesz potential and F(t)=∫0tf(τ)dτ is a general nonlinearity with a sublinear growth in the origin. The found decay is of polynomial type, with a rate possibly slower than [Formula presented], and it complements the decays obtained in the linear and superlinear cases in Cingolani et al. (2022); D'Avenia et al. (2015). Differently from the local case s=1 in Moroz and Van Schaftingen (2013), new phenomena arise connected to a new “s-sublinear” threshold that we detect on the growth of f. To gain the result we in particular prove a Chain Rule type inequality in the fractional setting, suitable for concave powers.
AB - Goal of this paper is to study the asymptotic behaviour of the solutions of the following doubly nonlocal equation (−Δ)su+μu=(Iα∗F(u))f(u)onRNwhere s∈(0,1), N≥2, α∈(0,N), μ>0, Iα denotes the Riesz potential and F(t)=∫0tf(τ)dτ is a general nonlinearity with a sublinear growth in the origin. The found decay is of polynomial type, with a rate possibly slower than [Formula presented], and it complements the decays obtained in the linear and superlinear cases in Cingolani et al. (2022); D'Avenia et al. (2015). Differently from the local case s=1 in Moroz and Van Schaftingen (2013), new phenomena arise connected to a new “s-sublinear” threshold that we detect on the growth of f. To gain the result we in particular prove a Chain Rule type inequality in the fractional setting, suitable for concave powers.
KW - Asymptotic behaviour
KW - Concave chain-rule
KW - Double nonlocality
KW - Fractional Laplacian
KW - Hartree term
KW - Nonlinear Choquard equation
KW - Sublinear nonlinearity
KW - Asymptotic behaviour
KW - Concave chain-rule
KW - Double nonlocality
KW - Fractional Laplacian
KW - Hartree term
KW - Nonlinear Choquard equation
KW - Sublinear nonlinearity
UR - http://hdl.handle.net/10807/268559
UR - https://www.sciencedirect.com/science/article/pii/s0362546x24000348
U2 - 10.1016/j.na.2024.113515
DO - 10.1016/j.na.2024.113515
M3 - Article
SN - 0362-546X
VL - 242
SP - 1
EP - 21
JO - NONLINEAR ANALYSIS
JF - NONLINEAR ANALYSIS
ER -