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

• Feng, Ren-Ting ^[1] ; Tang, Chun-Lei ^[1]
  1. [1] Southwest University

     Southwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
• DOI: 10.1007/s12346-021-00529-y
• Enlaces
  • Texto completo
• Resumen

  • 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).

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