Ground State Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

• Quanqing Li ^[1] ; Jian Zhang ^[3] ; Jianjun Nie ^[2]
  1. [1] Honghe University

     Honghe University

     China

     
  2. [2] North China Electric Power University

     North China Electric Power University

     China

     
  3. [3] University of Craiova & Hunan University of Technology and Business

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • In this paper, we study the following generalized quasilinear Schrödinger equation with critical growth −div(g2(u)∇u) + g(u)g (u)|∇u| 2 + V(x)u = λ f (x, u) + |u| α2∗−2u, x ∈ RN , where λ > 0, N ≥ 3, g : R → R+ is a C1 even function, g(0) = 1, g (s) ≥ 0 for all s ≥ 0, g(s) = β|s| α−1 + O(|s| γ −1) as s → ∞ for some constants α ∈ [1, 2],β> 0, γ <α and (α − 1)g(s) ≥ g (s)s for all s ≥ 0. Under some suitable conditions on the potential and nonlinearity, we obtain the existence of ground state solutions for large λ by using dual approach and Nehari manifold method.