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Liouville Theorems for an Integral Equation of Choquard Type

Authors: 

Phuong Le

Source title: 
Communications On Pure and Applied Analysis, 19(2): 771-783, 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

We establish sharp Liouville theorems for the integral equation

a

where 0 < α, β < n and p > 1. Our results hold true for positive solutions under appropriate assumptions on p and integrability of the solutions. As a consequence, we derive a Liouville theorem for positive b solutions of the higher fractional order Choquard type equation

c