Liouville‐type theorem for finite Morse index solutions to the Choquard equation involving Δλ‐Laplacian

摘要

In this paper, we are concerned with the following Choquard‐type equation: −Δλu=∫ℝN|y|λβ|u(y)|p|x−y|λαdy|x|λβ|u(x)|p−2u(x)inℝN,$$ -{Delta}_{lambda }u={int}_{{mathbb{R}}^N}frac{{left|yright|}_{lambda}^{beta }{left|u(y)right|}^p}{{left|x-yright|}_{lambda}^{alpha }} dy{left|xright|}_{lambda}^{beta }{left|u(x)right|}^{p-2}u(x)kern6.05pt mathrm{in}kern6.05pt {mathbb{R}}^N, $$ where N,p>2$$ N,p2 $$, 0<α