NONSTATIONARY HOMOCLINIC ORBIT FOR AN INFINITE-DIMENSIONAL FRACTIONAL REACTION-DIFFUSION SYSTEM

被引：3
|
作者：
Chen, Peng [1 ]
Mei, Linfeng [2 ,3 ]
Tang, Xianhua [2 ,3 ]
机构：
[1] China Three Gorges Univ, Three Gorges Math Res Ctr, Yichang 443002, Hubei, Peoples R China
[2] Zhejiang Normal Univ, Coll Math & Comp Sci, Jinhua 321004, Zhejiang, Peoples R China
[3] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年 / 27卷 / 10期
关键词：
Reaction-diffusion system; homoclinic orbit; strongly indefinite functional; non-Nehari manifold method; boundedness of Cerami sequences; NEHARI-MANIFOLD METHOD;
D O I：
10.3934/dcdsb.2021279
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper study nonstationary homoclinic-type solutions for a fractional reaction-diffusion system with asymptotically linear and local super linear nonlinearity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite, the second lies in verifying the link geometry and showing the boundedness of Cerami sequences when the nonlinearity is not super quadratic at infinity globally. These enable us to develop a direct approach and new tricks to overcome the difficulties. We establish the existence of homoclinic orbit under some weak assumptions on nonlinearity.
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页码：5389 / 5409
页数：21
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