scholarly journals An eigenvalue problem for nonlinear Schrödinger-Poisson system with steep potential well

2021 ◽  
Vol 20 (4) ◽  
pp. 1497
Author(s):  
Kuan-Hsiang Wang
Keyword(s):  
Eigenvalue Problem ◽  
Potential Well ◽  
Poisson System ◽  
Nonlinear Schrödinger ◽  
Steep Potential Well

NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL

2001 ◽  
Vol 03 (04) ◽  
pp. 549-569 ◽  
Author(s):  
THOMAS BARTSCH ◽  
ALEXANDER PANKOV ◽  
ZHI-QIANG WANG
Keyword(s):  
Essential Spectrum ◽  
Model Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Potential Well ◽  
Local Minima ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Steep Potential Well

We investigate nonlinear Schrödinger equations like the model equation [Formula: see text] where the potential Vλ has a potential well with bottom independent of the parameter λ > 0. If λ → ∞ the infimum of the essential spectrum of -Δ + Vλ in L2(ℝN) converges towards ∞ and more and more eigenvalues appear below the essential spectrum. We show that as λ→∞ more and more solutions of the nonlinear Schrödinger equation exist. The solutions lie in H1(ℝN) and are localized near the bottom of the potential well, but not near local minima of the potential. We also investigate the decay rate of the solutions as |x|→∞ as well as their behaviour as λ→∞.

scholarly journals Schrödinger–Poisson system with steep potential well

2011 ◽  
Vol 251 (3) ◽  
pp. 582-608 ◽  
Author(s):  
Yongsheng Jiang ◽  
Huan-Song Zhou
Keyword(s):  
Potential Well ◽  
Poisson System ◽  
Steep Potential Well
Sign in / Sign up

Export Citation Format

Share Document