scholarly journals Multiple minimal nodal solutions for a quasilinear Schrödinger equation with symmetric potential

2005 ◽  
Vol 304 (1) ◽  
pp. 170-188 ◽  
Author(s):  
Marcelo F. Furtado
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nodal Solutions ◽  
Quasilinear Schrödinger Equation ◽  
Symmetric Potential

Least Energy Nodal Solutions for a Defocusing Schrödinger Equation with Supercritical Exponent

2018 ◽  
Vol 62 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Minbo Yang ◽  
Carlos Alberto Santos ◽  
Jiazheng Zhou
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Positive Function ◽  
Nehari Manifold ◽  
Nodal Solution ◽  
Nodal Solutions ◽  
Quasilinear Schrödinger Equation ◽  
Subcritical Growth ◽  
Image Position ◽  
Least Energy

AbstractIn this paper we consider the existence of least energy nodal solution for the defocusing quasilinear Schrödinger equation $$-\Delta u - u \Delta u^2 + V(x)u = a(x)[g(u) + \lambda \vert u \vert ^{p-2}u] \hbox{in} {\open R}^N,$$ where λ≥0 is a real parameter, V(x) is a non-vanishing function, a(x) can be a vanishing positive function at infinity, the nonlinearity g(u) is of subcritical growth, the exponent p≥22*, and N≥3. The proof is based on a dual argument on Nehari manifold by employing a deformation argument and an $L</italic>^{\infty}({\open R}^{N})$-estimative.

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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