Classification of Stable Solutions to a Fractional Elliptic Equations with Robin boundary value

In this article, we study the nonexistence of solution with finite Morse index for the following nonlinear elliptic equation for fractional Laplacian : (−∆) s u + λu = |u| p−1 u in R n + with ∂u/∂ν + cu = 0 on ∂R n +. where n ≥ 2s, 0 < s 1. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula. PACS: Primary : 35J55, 35J65 ; Secondary : 35B65.