Infinitely many solutions for a new Kirchhoff-type equation with subcritical exponent

In this article, we consider the following new Kirchhoff-type problem: −a−b∫Ω|∇u|2dxΔu=|u|p−2,in Ω,u=0,on ∂Ω, where a and b are positive constants, Ω⊂RN is a bounded domain with C1 boundary ∂Ω, p∈[2,2∗) with 2∗=2N/(N−2) if N≥3, and 2∗=+∞ if N = 1, 2. We show that the problem possesses infinitely many sign-changing solutions by using combination of invariant sets of descent flow and the Ljusternik–Schnirelman type minimax method. And an example for p = 2 is illustrated our results.