Recurrent solutions of the derivative Ginzburg–Landau equation with boundary forces

ABSTRACT

In this paper, we will establish the existence of the bounded solutions, periodic solutions, quasi-periodic solutions and almost periodic solutions for the derivative Ginzburg–Landau equation with time-dependent boundary external forces. A smoothing effect for the semigroup associated with linear Ginzburg–Landau operator is the crucial tool in establishing the main results.

Keywords:

• The derivative Ginzburg–Landau equation
• bounded solutions
• periodic solutions
• quasi-periodic solutions
• almost periodic solutions

AMS Subject Classifications:

• 35K55
• 35Q55
• 70K43
• 35B10
• 35B15

Acknowledgements

I would like to thank the referees and the editor for their careful comments and useful suggestions. I sincerely thank my PhD supervisor professor Yong Li for many useful suggestions and help.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by NSFC [grant number 11601073] and the Fundamental Research Funds for the Central Universities [grant number 2412016KJ012].