Existence and asymptotic behaviour of positive solutions for semilinear polyharmonic coupled systems

Abstract

Let m be a positive integer. We investigate the existence and the asymptotic behaviour of positive continuous solutions to the following coupled polyharmonic system in the unit ball B of , ,

where , , r, such that and the functions a, b are nonnegative measurable on B satisfying some assumptions related to Karamata regular variation theory.

Keywords:

• Polyharmonic elliptic system
• positive solution
• Kato class
• Karamata function
• asymptotic behaviour
• Schäuder fixed point theorem

AMS Subject Classifications:

• 35J48
• 35J58
• 35B09
• 35B40

Acknowledgements

The authors thank the referee for his or her careful reading of the paper and helpful comments and remarks.

Notes

No potential conflict of interest was reported by the authors.