On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍ n

This article is devoted to the study of a critical Choquard-Kirchhoff <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -sub-Laplacian equation on the entire Heisenberg group <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">H</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:math> {{H}}ⁿ , where the Kirchhoff function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>K</m:mi> </m:math> K 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.