Multiplicity of solutions for the Kirchhoff equation with critical nonlinearity in high dimension

This paper is devoted to the following Kirchhoff type of problems: where Ω is a smooth bounded domian in , a > 0, b > 0 are real constants, , q ∈ [1, 2 ∗ − 1), . Under some suitable assumptions on V ( x ), we will prove the multiplicity of solutions for the Kirchhoff‐type equation by the variational method.