scholarly journals Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent

2012 ◽  
Vol 205 (2) ◽  
pp. 515-551 ◽  
Author(s):  
Zhijie Chen ◽  
Wenming Zou
Keyword(s):  
Phase Separation ◽  
Critical Exponent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Least Energy Solutions ◽  
Least Energy

Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Zhongwei Tang ◽  
Lushun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Laplacian ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Definition Of ◽  
Least Energy Solutions ◽  
Least Energy

AbstractIn this paper, we consider a class of Schrödinger equations involving fractional Laplacian and indefinite potentials. By modifying the definition of the Nehari–Pankov manifold, we prove the existence and asymptotic behavior of least energy solutions. As the fractional Laplacian is nonlocal, when the bottom of the potentials contains more than one isolated components, the least energy solutions may localize near all the isolated components simultaneously. This phenomenon is different from the Laplacian.

Sign in / Sign up

Export Citation Format

Share Document