Liouville Theorem for Some Elliptic Equations with Weights and Finite Morse Indices

Abstract

We establish the nonexistence of solution for the following nonlinear elliptic problem with weights: -Δu=(1+|x|α)|u|p-1u in RN, where α is a positive parameter. Suppose that 1(N-2)(p+1)/2-N for N≥3 or p>1, α>-2 for N=2; we will show that this equation does not possess nontrivial bounded solution with finite Morse index.