Existence of multiple solutions for a p-Kirchhoff problem with the non-linear boundary condition

ABSTRACT

In this paper, using the Nehari manifold and fibering maps, we study the existence of at least two positive solutions for the following p-Kirchhoff equation

where is a bounded domain, with a, b, , is the p-Laplacian operator, is a parameter.

Keywords:

• p-Kirchhoff equation
• nonlinear boundary condition
• multiple solutions
• ehari manifold

AMS Subject Classifications:

• 35A15
• 35B38
• 35J65

Acknowledgements

The authors would like to express sincere thanks to the anonymous referee for his/her carefully reading the manuscript and valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Project Supported by the Natural Science Foundation of Education Bureau of Anhui Province [grant number KJ2017A432]; and the NSF of China [grant number 11571093], [grant number 11471164].