Resumen de Normalized Solutions to the Fractional Schrödinger Equation with Critical Growth
Xinsi Shen, Ying Lv, Zengqi Ou
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.
