Least Energy Solutions of the Schrödinger–Kirchhoff Equation with Linearly Bounded Nonlinearities

• Yanyan Liu ^[1] ; Leiga Zhao ^[1]
  1. [1] Beijing Technology and Business University

     Beijing Technology and Business University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we consider the following Schrödinger–Kirchhoff equation − a + b RN |∇u| 2 dx u + V(x)u = f (x, u), in RN , where N ≥ 3, a and b are positive parameters, V(x) is a positive and continuous potential. Under some suitable assumptions on the nonlinearity f (x, u) which allow it is linearly bounded at infinity, the existence of least energy solutions and their asymptotic behavior as b → 0 are established via variational methods. The nonexistence of nontrivial solutions is also established for large b.