Existence of solutions for asymptotically periodic fractional Schrödinger equation with critical growth

2020 ◽  
Vol 43 (17) ◽  
pp. 10081-10097
Author(s):  
Yongzhen Yun ◽  
Tianqing An ◽  
Guoju Ye ◽  
Jiabin Zuo
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Existence Of Solutions ◽  
Critical Growth ◽  
Fractional Schrödinger Equation ◽  
Asymptotically Periodic ◽  
Fractional Schrodinger Equation

scholarly journals The Existence of Normalized Solutions for a Nonlocal Problem in ℝ3

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jing Yang
Keyword(s):  
Schrödinger Equation ◽  
Variational Method ◽  
Schrodinger Equation ◽  
Existence Of Solutions ◽  
Nonlocal Problem ◽  
Fractional Schrödinger Equation ◽  
Normalized Solutions ◽  
Fractional Schrodinger Equation

In this paper, we study the following fractional Schrödinger equation in ℝ3−Δσu−λu=up−2u, in ℝ3 with σ∈0,1,λ∈ℝ and p∈2+σ,2+4/3σ. By using the constrained variational method, we show the existence of solutions with prescribed L2 norm for this problem.

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