Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system

Peng Chen; Linfeng Mei; Xianhua Tang

doi:10.3934/dcdsb.2021279

Article Contents

2022, Volume 27, Issue 10: 5389-5409. Doi: 10.3934/dcdsb.2021279

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Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system

1.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, China
2.
College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
3.
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China

^* Corresponding author: Linfeng Mei
^* Corresponding author: Linfeng Mei

Received: July 31, 2021

Early access: November 2021

Published: October 2022

The first author is supported by the Natural Science Foundation of Hubei Province of China: Grant No. 2021CFB473, the second author is supported by the Natural Science Foundation of China: Grant No. 11771125

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Abstract

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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Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 35Q55.

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