Entire solutions of a public goods game model

Abstract

This paper is concerned with the entire solutions defined in the whole space and for all time $t\in \mathbb{R}$ of a public good game model. The existence of the entire solutions is proved by super- and sub-solution method. Traveling fronts with possibly different wave speeds are used to construct the super- and sub-solutions, in particular, the traveling fronts of a variant of KPP equation are used to derive the t < 0 part of the super solutions.

COMMUNICATED BY:

• M. Mei

Keywords:

• Entire solution
• traveling front
• sub-super solution

AMS Subject classifications:

• 35K57
• 35B08
• 35B40

Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments and many useful suggestions on better presentation and revision of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author is supported by Natural Science Foundation of China (NSF of China) 11501016, 11871048 and Beijing Natural Science Foundation (Beijing NSF) (1172005). The third author is supported by NSF of China (11801314).