Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system

Abstract

In this paper, we consider the quasilinear Schrödinger system in ${\mathbb{R}}^N$($N\ge 3$): $$\{\begin{array}{rl}& -\Delta u+A(x)u-\frac{1}{2}△(u^2)u=\frac{2\alpha }{\alpha +\beta }|u{|}^{\alpha -2}u|v{|}^{\beta },\\ & -\Delta v+Bv-\frac{1}{2}△(v^2)v=\frac{2\beta }{\alpha +\beta }|u{|}^{\alpha }|v{|}^{\beta -2}v,\end{array}$$ where $\alpha ,\beta >1$, $2<\alpha +\beta <\frac{4N}{N-2}$,$B>0$ is a constant. By using a constrained minimization on Nehari-Pohožaev set, for any given integer $s\ge 2$, we construct a non-radially symmetrical nodal solution with its $2s$ nodal domains.

arXiv admin note: substantial text overlap with arXiv:2305.14911, arXiv:2305.15449