scholarly journals Least energy solutions for nonlinear Schrödinger equation involving the fractional Laplacian and critical growth

2017 ◽  
Vol 37 (7) ◽  
pp. 3963-3987
Author(s):  
Zhongwei Tang ◽  
Miaomiao Niu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fractional Laplacian ◽  
Nonlinear Schrodinger Equation ◽  
Critical Growth ◽  
Nonlinear Schrödinger ◽  
Least Energy Solutions ◽  
Least Energy

A symmetry-breaking phenomenon and asymptotic profiles of least-energy solutions to a nonlinear Schrödinger equation

2005 ◽  
Vol 135 (2) ◽  
pp. 357-392 ◽  
Author(s):  
Kazuhiro Kurata ◽  
Tatsuya Watanabe ◽  
Masataka Shibata
Keyword(s):  
Schrödinger Equation ◽  
Symmetry Breaking ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Least Energy Solution ◽  
Image Position ◽  
Least Energy Solutions ◽  
Least Energy

In this paper, we study a symmetry-breaking phenomenon of a least-energy solution to a nonlinear Schrödinger equation under suitable assumptions on V(x), where λ > 1, p > 2 and χA is the characteristic function of the set A = [−(l + 2), −l] ∪ [l,l + 2] with l > 0. We also study asymptotic profiles of least-energy solutions for the singularly perturbed problem for small ε > 0.

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