Existence of ground state for fractional Kirchhoff equation with L 2 $L^{2}$ critical exponents

Abstract

Abstract In this paper, we consider a class of fractional Kirchhoff equations with L 2 $L^{2}$ critical exponents. By using the scaling technique and concentration-compactness principle we obtain the existence and nonexistence of ground state for fractional Kirchhoff equation with L 2 $L^{2}$ critical exponent.

Keywords

• L 2 $L^{2}$ critical exponent
• Besov space
• Fractional Kirchhoff equation
• Ground state