Resumen de Ground State Sign-Changing Solutions for a Kirchhoff Equation with Asymptotically 3-Linear Nonlinearity

Ren-Ting Feng, Chun-Lei Tang

• In this paper, we investigate the following nonlinear Kirchhoff equation −(a+b∫R3|∇u|2dx)△u+V(x)u=f(u),x∈R3, where a, b are positive constants, V is a potential and f∈C(R3×R,R) is an asymptotically 3-linear nonlinearity. By using sign-changing Nehari manifold, we can not only get the existence of ground state sign-changing solution under the condition of b>0. but also can prove that its energy is strictly larger than twice that of ground state solutions. In addition, we obtain a convergence property of ubn as bn→0. In this article, we present weaker hypotheses than those that can be found (Xie in Adv Differ Equ 121:1–14, 2016).