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

Abstract

Under some general conditions of 𝜆 i , we prove that the equation has no nontrivial solution which is stable outside a compact set in the subcritical casewhere Q is the homogeneous dimension of R N associated to Δ 𝜆 . In addition, for the critical case p = 2Q−𝛼+2𝛽 Q−2 , we shall show that any solution u of the equation above, which is stable outside a compact set, has finite energy. More precisely, we show that