scholarly journals Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

Nonlinearity ◽  
2021 ◽  
Vol 34 (6) ◽  
pp. 4017-4056
Author(s):  
S Cingolani ◽  
M Gallo ◽  
K Tanaka
Keyword(s):  
Scalar Field ◽  
Lagrangian Formulation ◽  
Field Equations ◽  
Nonlinear Scalar Field ◽  
Normalized Solutions ◽  
Scalar Field Equations

scholarly journals Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter

2019 ◽  
Vol 150 (5) ◽  
pp. 2417-2441 ◽  
Author(s):  
Takafumi Akahori ◽  
Slim Ibrahim ◽  
Hiroaki Kikuchi
Keyword(s):  
Scalar Field ◽  
Ground State ◽  
Linear Instability ◽  
Frequency Parameter ◽  
Field Equations ◽  
Power Type ◽  
Nonlinear Scalar Field ◽  
Scalar Field Equations ◽  
Sobolev Critical Exponent ◽  
Large Frequency

AbstractWe consider combined power-type nonlinear scalar field equations with the Sobolev critical exponent. In [3], it was shown that if the frequency parameter is sufficiently small, then the positive ground state is nondegenerate and linearly unstable, together with an application to a study of global dynamics for nonlinear Schrödinger equations. In this paper, we prove the nondegeneracy and linear instability of the ground state frequency for sufficiently large frequency parameters. Moreover, we show that the derivative of the mass of ground state with respect to the frequency is negative.

Sign in / Sign up

Export Citation Format

Share Document