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

Abstract

In this paper, we study the following quasilinear Schrödinger equations −Δu−Δ(|u|2α)|u|2α−2u=ω(x)|u|q−1u,x∈ℝN, where α>12 is a parameter, q>3α−1+α2α, ωfalse(xfalse)∈Cfalse(ℝN\false{0false}false) 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.