scholarly journals A positive solution for an asymptotically cubic quasilinear Schrödinger equation

2019 ◽  
Vol 18 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Xiang-Dong Fang ◽  
Keyword(s):  
Schrödinger Equation ◽  
Positive Solution ◽  
Schrodinger Equation ◽  
Quasilinear Schrödinger Equation ◽  
Asymptotically Cubic

Bifurcation and standing wave solutions for a quasilinear Schrödinger equation

2018 ◽  
Vol 149 (04) ◽  
pp. 939-968
Author(s):  
Guowei Dai
Keyword(s):  
Schrödinger Equation ◽  
Positive Solution ◽  
Standing Wave ◽  
Positive Solutions ◽  
Schrodinger Equation ◽  
Quasilinear Schrödinger Equation ◽  
Topological Methods ◽  
Wave Solutions ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

AbstractWe use bifurcation and topological methods to investigate the existence/nonexistence and the multiplicity of positive solutions of the following quasilinear Schrödinger equation$$\left\{ {\matrix{ {-\Delta u-\kappa \Delta \left( {u^2} \right)u = \beta u-\lambda \Phi \left( {u^2} \right)u{\mkern 1mu} {\mkern 1mu} } \hfill & {{\rm in}\;\Omega ,} \hfill \cr {u = 0} \hfill & {{\rm on}\;\partial \Omega } \hfill \cr } } \right.$$involving sublinear/linear/superlinear nonlinearities at zero or infinity with/without signum condition. In particular, we study the changes in the structure of positive solution withκas the varying parameter.

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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