Ground states of degenerate quasilinear Schrödinger equation with vanishing potentials

2019 ◽  
Vol 189 ◽  
pp. 111587 ◽  
Author(s):  
Olimpio H. Miyagaki ◽  
Cláudia R. Santana ◽  
Rônei S. Vieira
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Ground States ◽  
Quasilinear Schrödinger Equation ◽  
Vanishing Potentials

MORAWETZ AND INTERACTION MORAWETZ ESTIMATES FOR A QUASILINEAR SCHRÖDINGER EQUATION

2012 ◽  
Vol 09 (04) ◽  
pp. 613-639 ◽  
Author(s):  
ALESSANDRO SELVITELLA ◽  
YUN WANG
Keyword(s):  
Schrödinger Equation ◽  
Plasma Physics ◽  
Schrodinger Equation ◽  
Energy Space ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation

We extend the classical Morawetz and interaction Morawetz machinery to a class of quasilinear Schrödinger equations coming from plasma physics. As an application of our main results we ensure the absence of pseudosolitons in the defocusing case. Our estimates are the first step to a scattering result in the energy space for this equation.

Existence of a Ground State Solution for a Quasilinear Schrödinger Equation

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Xiang-dong Fang ◽  
Zhi-qing Han
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Quasilinear Schrödinger Equation

AbstractIn this paper we are concerned with the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere N ≥ 3, 4 < p < 4N/(N − 2), and V(x) and q(x) go to some positive limits V

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