Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains

Abstract

We are interested in the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem in bounded domains. Because the so-called nonlocal term b(∫Ω|∇u|2dx)Δu is involving in the equation, the variational functional of the equation has totally different properties from the case of b=0. Combining constraint variational method and quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution ub. Moreover, we show that the energy of ub is strictly larger than the ground state energy. Finally, we regard b as a parameter and give a convergence property of ub as b↘0.