Existence of ground state solutions for a super-biquadratic Kirchhoff-type equation with steep potential well

Abstract

In this paper, we concern with the following Kirchhoff-type problem

where are constants, is a parameter, is a nonnegative continuous potential, and is a subcritical growth nonlinearity. Under appropriate assumptions on and , we prove the existence of ground state solutions using variational methods. Furthermore, we also study the asymptotic behavior of ground state solutions.

Keywords:

• Kirchhoff-type equation
• ground state solution
• Nehari manifold
• variational method

AMS Subject Classifications:

• 35J91
• 35J20
• 47J30

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.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Science Foundation of China [grant number 11171135], [grant number 51276081], [grant number 11201186], [grant number 11371090]; Major Project of Natural Science Foundation of Jiangsu Province Colleges and Universities [grant number 14KJA110001]; Natural Science Foundation of Jiangsu Province [grant number BK20140106], [grant number BK2012282], [grant number BK2010420], [grant number BK2010329]; Jiangsu University Foundation [grant number 11JDG117]; China Postdoctoral Science Foundation funded project [grant number 2012M511199], [grant number 2013T60499]; Doctoral Fund of Ministry of Education of China [grant number 20093227110012].