Positive radial solutions for a class of quasilinear Schrödinger equations in $\mathbb{R}^3$

Abstract

This paper is concerned with the following quasilinear Schrödinger equations of the form: \begin{equation*} -\Delta u-u\Delta (u^2)+u=|u|^{p-2}u, \qquad x\in \mathbb{R}^3, \end{equation*} where $p\in\left(2,12\right)$. By making use of the constrained minimization method on a special manifold, we prove that the existence of positive radial solutions of the above problem for any $p\in(2,12)$.

Keywords

• quasilinear schrödinger equations
• constrained minimization method