Ground State Sign-Changing Solutions for Schrödinger-Kirchhoff Equation with Asymptotically Cubic or Supercubic Nonlinearity

• Cai-Ni Yang ^[1] ; Chun-Lei Tang ^[1]
  1. [1] Southwest University

     Southwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.

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