Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system

Abstract

In this paper, we consider the quasilinear Schrödinger system in $\mathbb R^{N}$ ($N\geq3$): \begin{equation*} \begin{cases} -\Delta u+ A(x)u-\frac{1}{2}\Delta(u^{2})u=\frac{2\alpha }{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+ Bv-\frac{1}{2}\Delta(v^{2})v=\frac{2\beta }{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v, \end{cases} \end{equation*} where $\alpha,\beta>1$, $20$ is a constant. By using a constrained minimization on Nehari–Pohožaev set, for any given integer $s\geq2$, we construct a non-radially symmetrical nodal solution with its $2s$ nodal domains.

Keywords

• quasilinear schrödinger system
• nehari–pohožaev set
• non-radially symmetrical nodal solutions.