Abstract: We considered the existence of positive ground state solutions for a class of critical Kirchhoff-Choquard type problems. Firstly, we used the properties and integral estimates of the truncated function to classify the upper critical exponents, and applied some integrable conditions to the potential function. Secondly, by introducing the Nehari manifold and utilizing the Ekeland variational principle, we obtain that there is at least one positive ground state solution to the problems under appropriate parameter assumptions.

Key words: Kirchhoff-Choquard type problem, critical exponent, Nehari manifold, positive ground state solution