Infinitely many solutions for a class of fractional Kirchhoff problems with critical exponent

We study a class of nonlocal Kirchhoff-type problems involving the fractional p p -Laplacian and critical Sobolev growth. The equation includes a Kirchhoff term M(t) = a + tᵐ M ( t ) = a + t m , with a ≥ 0 a ≥ 0 and $$ m > 0 $$ m > 0 , and is posed on a bounded domain with Lipschitz boundary. Using variational methods, Krasnoselskii’s genus theory, and a fractional concentration-compactness principle, we prove the existence of infinitely many weak solutions in both the non-degenerate ( $$ a > 0 $$ a > 0 ) and degenerate ( $$ a = 0 $$ a = 0 ) cases.