Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction

• Published in: Electronic research archive Vol. 31; no. 4; pp. 2071 - 2094
• Main Authors: Wang, Yixuan, Huang, Xianjiu
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: ground state solutions; pohožaev manifold; quasilinear schrödinger systems
• ISSN: 2688-1594; 2688-1594
• DOI: 10.3934/era.2023106

This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition: <disp-formula> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{\begin{matrix} -\Delta u+V_{1}(x)u-\Delta (u^{2})u = h(u,v),\ x\in \mathbb{R}^{N},\\ -\Delta v+V_{2}(x)v-\Delta (v^{2})v = g(u,v),\ x\in \mathbb{R}^{N},\\ \end{matrix}\right. \end{equation*} $\end{document} </tex-math></disp-formula> where $ N \geq3 $, $ V_{1}(x) $, $ V_{2}(x) $ are variable potentials and $ h $, $ g $ satisfy some conditions. By establishing a suitable Nehari-Pohožaev type constraint set and considering related minimization problem, we prove the existence of ground states.