Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system. (Q2662469)

The authors study the following quasilinear Schrödinger system in the entire space \(\mathbb{R}^N\) \((N\geq 3)\):\[\begin{cases}-\Delta u+A(x)u-\frac{1}{2} \triangle(u^{2})u=\frac{2\alpha}{\alpha+\beta} |u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v.\end{cases}\] By establishing a suitable constraint set and studying related minimization problem, they prove the existence of a ground state solution for \(\alpha,\beta >1\), \(2<\alpha+\beta<\frac{4N}{N-2}\). Their results can be looked on as a generalization of results by \textit{Y. Guo} and \textit{Z. Tang} [J. Math. Anal. Appl. 389, No. 1, 322--339 (2012; Zbl 1236.35036)].