On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn

Abstract

This article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving a nonlinearity, which is critical in the sense of the Hardy-Littlewood-Sobolev inequality. We first establish the concentration-compactness principle for the pp-sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.

Keywords

• heisenberg group
• choquard-kirchhoff equation
• hardy-littlewood-sobolev critical exponent
• concentration-compactness principle
• variational methods
• 35j20
• 35r03
• 46e35