Normalized Solutions to the Fractional Schrödinger Equation with Critical Growth

• Xinsi Shen ^[1] ; Ying Lv ^[1] ; Zengqi Ou ^[1]
  1. [1] Southwest University

     Southwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-00995-0
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we discuss the existence of normalized solutions to the following fractional Schrödinger equation (−)su = λu + g(u) + |u| 2∗ s −2u, x ∈ RN , RN u2 = a2, where N ≥ 3, s ∈ (0, 1), a > 0, 2∗ s = 2N/(N − 2s), λ ∈ R arises as a Lagrange multiplier, (−)s is the fractional Laplace operator and g : R → R satisfies L2- supercritical conditions. The proof is based on a constrained minimization method and some characterizations of the mountain pass levels are given in order to prove the existence of ground state normalized solutions.

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