Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent

Abstract

Abstract In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative energy solutions. Also, we prove some further properties of solutions.

Keywords

• Fractional equation
• Kirchhoff type
• Hardy–Littlewood–Sobolev critical exponent
• Multiple solution