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Journal of Dynamical and Control Systems

Erschienen in:

24.04.2018

Existence and Multiplicity of Standing Wave Solutions for a Class of Quasilinear Schrödinger Systems in $\mathbb {R}^{N}$

verfasst von: Hongxue Song, Caisheng Chen, Wei Liu

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 1/2019

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Abstract

In this paper, we study the following quasilinear Schrödinger systems of the form

$$\begin{array}{@{}rcl@{}} \left\{\begin{array}{l} -\triangle_{p} u_{j}+a_{j}(x)|u_{j}|^{p-2}u_{j}\,-\,\triangle_{p} (|u_{j}|^{2})u_{j}\,=\,\mu_{j}|u_{j}|^{q-2}u_{j}\,+\,\frac{1}{2}{\sum}_{i\neq j}\beta_{ij}|u_{i}|^{m}|u_{j}|^{m-2}u_{j}, ~x\!\in\! \mathbb{R}^{N},\\ u_{j}(x)\rightarrow 0,~\text{as} ~|x|\rightarrow \infty, \ j = 1,\ \cdots,\ k, \end{array} \right. \end{array} $$

(0.1)

where N ≥ 3, 2 ≤ p ≤ N, and the potential a_j(x) is positive and bounded in $\mathbb {R}^{N}$, μ_j > 0, β_ij = β_ji for 1 ≤ i < j ≤ k(k ≥ 2). Using symmetric mountain pass lemma, we obtain infinitely many solutions to Schrödinger system (0.1).

Vorheriger Artikel Pseudo Almost Periodic Solutions to Impulsive Non-autonomous Stochastic Differential Equations with Unbounded Delay and its Optimal Control

Nächster Artikel Global Attractor for a Class of Sixth-Order Viscous Cahn-Hilliard Equation in an Unbounded Domain

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Titel: Existence and Multiplicity of Standing Wave Solutions for a Class of Quasilinear Schrödinger Systems in
verfasst von: Hongxue Song
Caisheng Chen
Wei Liu
Publikationsdatum: 24.04.2018
Verlag: Springer US
Erschienen in: Journal of Dynamical and Control Systems / Ausgabe 1/2019
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-018-9399-6

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