Least energy sign-changing solutions of Kirchhoff-type equation with critical growth

Abstract

In this paper, we study the Kirchhoff-type equation −(a + b∫Ω|∇u|2dx)Δu = |u|4u + λf(x, u), x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω⊂R3 is a bounded domain with a smooth boundary ∂Ω, λ, a, b > 0. Under suitable conditions on f, by using the constraint variational method and the quantitative deformation lemma, if λ is large enough, we obtain a least energy sign-changing (or nodal) solution ub to this problem for each b > 0. Moreover, we prove that the energy of ub is strictly larger than twice that of the ground state solutions.

Topics & Concepts