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Stable Solutions to the Static Choquard Equation

Stable Solutions to the Static Choquard Equation

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

where * N, p *>

**2**and

**max{0,**. We prove that if

*N −*4} < α < N**u**∈

**C**is 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

^{1}

**α ≠****2**.