scholarly journals Standing waves with a critical frequency for nonlinear Schrödinger equations involving critical growth

2017 ◽  
Vol 63 ◽  
pp. 53-58 ◽  
Author(s):  
Jianjun Zhang
Keyword(s):  
Critical Frequency ◽  
Standing Waves ◽  
Critical Growth ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

Standing waves with a critical frequency for a quasilinear Schrödinger equation

2019 ◽  
Vol 22 (08) ◽  
pp. 1950070
Author(s):  
Xiang-Dong Fang
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Critical Frequency ◽  
Standing Waves ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

We consider the following quasilinear Schrödinger equation [Formula: see text] where [Formula: see text], [Formula: see text], and [Formula: see text] satisfies a weaker growth condition than the Ambrosetti–Rabinowitz type condition in Byeon and Wang [Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal. 165(4) (2002) 295–316; Standing waves with a critical frequency for nonlinear Schrödinger equations, II, Calc. Var. 18(2) (2003) 207–219]. We obtain the existence of the localized bound state solutions concentrating at an isolated component of the local minimum of [Formula: see text] and whose amplitude goes to 0 as [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document