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Stable Solutions to the Static Choquard Equation

Authors: 

PHUONG LE

Source title: 
Bulletin of the Australian Mathematical Society, 102(3), 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

This paper is concerned with the static Choquard equation

a

where N, p > 2 and max{0, N − 4} < α < N. We prove that if u C1ais a stable weak solution of the equation, then u ≡ 0. This phenomenon is quite different from that of the local Lane–Emden equation, where such a result only holds for low exponents in high dimensions. Our result is the first Liouville theorem for Choquard-type equations with supercritical exponents and α ≠ 2.