Liouville theorem for Robin boundary value problems and finite Morse indices

In this paper, we study the nonexistence result of the following nonlinear elliptic equation with Robin boundary condition{−Δu=|u|p−1uin R+N,∂u∂ν+cu=0on ∂R+N. Under some assumptions on c and p, we will show that this problem does not possess nontrivial bounded solution with finite Morse index.