Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction
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},\\ -\Del...
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Published in | Electronic research archive Vol. 31; no. 4; pp. 2071 - 2094 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
AIMS Press
01.01.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 2688-1594 2688-1594 |
DOI: | 10.3934/era.2023106 |