Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

In this paper, we study the following quasilinear Schrödinger equations− Δ u − Δ ( | u | 2 α ) | u | 2 α − 2 u = ω ( x ) | u | q − 1 u , x ∈ ℝ N , where α > 1 2is a parameter, q > 3 α − 1 + α 2 α , ω ( x ) ∈ C ( ℝ N \ { 0 } ) is a positive function. We establish a Liouville type theorem for the class of stable bounded sign‐changing solutions under suitable assumptions on ω ( x ),  q ,  α and N .