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

Abstract EN

We establish the nonexistence of solution for the following nonlinear elliptic problem with weights: - Δ u = ( 1 + | x | α ) | u | p - 1 u in R N , where α is a positive parameter.

Suppose that 1 < p < N + 2 / N - 2 , α > ( 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.