Least energy nodal solutions for Kirchhoff-type problems involving the critical exponents

In this paper, we concern the existence of sign-changing solutions for the following Kirchhoff-type problems with critical growth: [Formula: see text] Here, [Formula: see text] is a smoothly bounded domain, [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Using the nodal Nehari manifold approach combined with the decomposition method, we prove the existence of least-energy nodal solutions for the above problem. Notably, the decomposition technique plays a crucial role in analyzing the lower bound of the energy functional in the sublinear case, i.e. [Formula: see text] and [Formula: see text], where the attainability of the infimum is demonstrated. This provides a key step in establishing the existence of nodal solutions. Moreover, by employing topological degree theory and the quantitative deformation lemma, we demonstrate that the minimizer obtained from the constrained set is indeed a nodal solution to the above problem.