Asymptotic behaviors of ground states for a modified Gross-Pitaevskii equation

Xiaoyu Zeng; Yimin Zhang

doi:10.3934/dcds.2019214

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2019, Volume 39, Issue 9: 5263-5273. Doi: 10.3934/dcds.2019214

This issue Previous Article Asymptotic spreading speed for the weak competition system with a free boundary Next Article Saddle-node of limit cycles in planar piecewise linear systems and applications

Asymptotic behaviors of ground states for a modified Gross-Pitaevskii equation

Xiaoyu Zeng and
Yimin Zhang^,

Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China

^* Corresponding author: Yimin Zhang
^* Corresponding author: Yimin Zhang

Received: August 31, 2018

Revised: February 28, 2019

Published: May 2019

The first author is supported by NSFC grants 11601173, 11871387 and the Fundamental Research Funds for the Central Universities(WUT: 2017 IVA 076). The second author is supported by NSFC grants 11671394, 11771127 and the Fundamental Research Funds for the Central Universities (WUT: 2018IB014)

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Abstract

In this paper, we consider $ L^2 $ constrained minimization problem for a modified Gross-Pitaevskii equation with higher order interactions in $ \mathbb{R}^2 $. By using an auxiliary functional and some detailed energy estimates, the blow-up behavior of ground state for the modified Gross-Pitaevskii equation was obtained under different parameter regimes. Our conclusion extends some results of [3,Theorem 3.4].

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Mathematics Subject Classification: 35J20, 35J60.

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