AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRÖDINGER EQUATIONS WITH SUPER-LINEAR NONLINEARITIES

2018 ◽  
Vol 99 (2) ◽  
pp. 231-241
Author(s):  
SITONG CHEN ◽  
ZU GAO
Keyword(s):  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions

By using variational and some new analytic techniques, we prove the existence of ground state solutions for the quasilinear Schrödinger equation with variable potentials and super-linear nonlinearities. Moreover, we establish a minimax characterisation of the ground state energy. Our result improves and extends the existing results in the literature.

scholarly journals New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory

2021 ◽  
pp. 1-17
Author(s):  
Yingying Xiao ◽  
Chuanxi Zhu
Keyword(s):  
Gauge Theory ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions ◽  
Chern Simons ◽  
Constraint Minimization

In this paper, we study the following quasilinear Schrödinger equation − Δ u + V ( x ) u − κ u Δ ( u 2 ) + μ h 2 ( | x | ) | x | 2 ( 1 + κ u 2 ) u + μ ( ∫ | x | + ∞ h ( s ) s ( 2 + κ u 2 ( s ) ) u 2 ( s ) d s ) u = f ( u ) in   R 2 , κ > 0 V ∈ C 1 ( R 2 , R ) and f ∈ C ( R , R ) By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions.

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.

Solitary Waves for Quasilinear Schrödinger Equations Arising in Plasma Physics

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
João Marcos do Ó ◽  
Abbas Moameni
Keyword(s):  
Schrödinger Equation ◽  
Plasma Physics ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation

AbstractWe study the quasilinear Schrödinger equationizwhere W : ℝ

Degenerate trajectories and Hamiltonian envelopes in the method of self-similar approximations

1993 ◽  
Vol 71 (11-12) ◽  
pp. 537-546 ◽  
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova
Keyword(s):  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
Approximate Calculation ◽  
State Energy ◽  
Anharmonic Oscillator ◽  
New Techniques ◽  
Self Similar ◽  
Very High

We study two new techniques for the approximate calculation of the eigenvalues of the Schrödinger equation. These techniques are variants of the method of self-similar approximations suggested recently by one of the authors. We illustrate the ideas by an anharmonic oscillator problem. We show that the precision of the method can be very high. For example, the ground-state energy of an anharmonic oscillator can be calculated with an error not exceeding 0.07% for all anharmonicity parameters ranging from zero to infinity.

Quasilinear Schrödinger Equations with Asymptotically Linear Nonlinearities

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Marcelo F. Furtado ◽  
Edcarlos D. Silva ◽  
Maxwell L. Silva
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonzero Solution ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Asymptotically Linear ◽  
Positive Potential ◽  
Quasilinear Schrödinger Equation

AbstractWe deal with the existence of nonzero solution for the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere V is a positive potential and the nonlinearity g(x, s) behaves like K

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