Resumen de Ground State Sign-Changing Solutions for Schrödinger-Kirchhoff Equation with Asymptotically Cubic or Supercubic Nonlinearity
Cai Ni Yang, Chun Lei Tang
In this paper, we investigate the existence of a least energy sign-changing solution for the following Schrödinger-Kirchhoff equation ⎧ ⎨ ⎩ −(a + b R3 |∇u| 2dx)u + V(x)u = f (x, u), x ∈ R3, u ∈ H1(R3) (SK) where a, b > 0 are parameters, V ∈ C(R3, R+) and f ∈ C(R3 ×R, R). The potential function V satisfies some suitable conditions and the nonlinearity f satisfies mild assumptions. By using sign-changing Nehari manifold, we prove that this problem possesses a ground state sign-changing solution with precisely two nodal domains, and its energy is strictly larger than twice that of ground state solutions. Besides, we obtain a convergence property of ubn as bn 0. Our results unify asymptotically cubic, which enrich and improve the previous ones in the literature.
