Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with \(H^{1}\)-supercritical exponent
This paper is concerned with the study of entire solutions of the nonlinear Schrödinger-type equation \[ -\Delta u+\lambda u-\kappa \Delta (|u|^\alpha)|u|^{\alpha -2}u=|u|^{p-1}u,\quad x\in {\mathbb R}^N \;(N\geq 3), \] where \(\alpha, p\in (1,\infty)\) and \(\lambda,\, \kappa\) are positive parameters. The first main result in this paper is concerned with the uniqueness and the non-degeneracy of the related zero mass problem. This property is useful in order to obtain the asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with \(H^1\)-supercritical exponent. The proofs combine a dual variational approach with ODE techniques.
scientific article; zbMATH DE number 6517096
scientific article