On the standing wave in coupled fractional Klein-Gordon equation

被引：0

作者：

Guo, Zhenyu ^{[1
]}

Zhang, Xin ^{[2
]}

机构：

[1] Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China

[2] Tongliao New City 1 Middle Sch, Tongliao 028000, Peoples R China

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2024年 / 31卷 / 03期

关键词：

Standing wave; ground state; fractional Klein-Gordon equations; GLOBAL EXISTENCE; NONEXISTENCE; INSTABILITY; SCHRODINGER; REGULARITY; STABILITY; SYSTEM;

D O I：

10.1515/gmj-2023-2089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to deal with the standing wave problems in coupled nonlinear fractional Klein-Gordon equations. First, we establish the constrained minimizations for a single nonlinear fractional Laplace equation. Then we prove the existence of a standing wave with a ground state using a variational argument. Next, applying the potential well argument and the concavity method, we obtain the sharp criterion for blowing up and global existence. Finally, we show the instability of the standing wave.

引用

页码：405 / 421

页数：17

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