Critical Kirchhoff (p,q)-equations with lack of compactness

In this entire space [Formula: see text], we investigate the existence and multiplicity of solutions to the critical Kirchhoff-type double-phase problems. This study addresses the comprehensive effects of critical terms alongside subcritical or singular reaction terms. Under the assumptions of suitable nonlinear exponents and Kirchhoff functions, we prove that there are infinitely many weak solutions with negative energy for a single-parameter problem when the parameter belongs to a certain interval. Moreover, we also prove that there is at least one positive energy solution for the single-parameter or double-parameter problem with proper parameters. Last but not least, since our results cover the degenerate case, it is also worth mentioning that the compactness issues are more delicate in the degenerate case. Our proofs use the variational methods and the principle of concentrated compactness.