Abstract 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.
Marcial et al. (Wed,) studied this question.