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

Yixuan Wang; Xianjiu Huang; Yixuan Wang; Xianjiu Huang

doi:10.3934/era.2023106

Electronic Research Archive

2023, Volume 31, Issue 4: 2071-2094. doi: 10.3934/era.2023106

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

Yixuan Wang ,
Xianjiu Huang ^,

School of Mathematics and Computer Sciences, Nanchang University, Nanchang, Jiangxi 330031, China

Received: 13 December 2022 Revised: 14 January 2023 Accepted: 25 January 2023 Published: 17 February 2023

This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition:

$ \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*} $

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.
- quasilinear Schrödinger systems,
- ground state solutions,
- Pohožaev manifold
Citation: Yixuan Wang, Xianjiu Huang. Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction[J]. Electronic Research Archive, 2023, 31(4): 2071-2094. doi: 10.3934/era.2023106

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Abstract

This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition:

$ \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*} $

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.

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