Semiclassical ground states for a class of nonlinear Kirchhoff-type problems

Abstract

In this paper, we study the following semilinear Kirchhoff-type equation

where is a parameter, a, b are positive constants, V and Q are positive bounded functions. For the equation with three times growth, we develop an argument to establish the existence of ground states for small. We also describe the concentration phenomena of ground states as .

Keywords:

• Kirchhoff-type equation
• concentration
• Nehari manifold
• semiclassical state

AMS Subject Classifications:

• 35J60
• 35J92
• 35A15

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Special Funds of the National Natural Science Foundation of China [grant number 11526103, 11571140]; the Natural Science Foundation of Jiangsu Province [grant number BK20140106]; the Natural Science Foundation for Outstanding Young Scholars of Jiangsu Province (BK20160063) and the Research Foundation of Jinling Institute of Technology [grant number jit-gjfh-201501].