scholarly journals Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well

2016 ◽  
Vol 57 (3) ◽  
pp. 031502 ◽  
Author(s):  
Miao Du ◽  
Lixin Tian ◽  
Jun Wang ◽  
Fubao Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Nonlinear Schrödinger ◽  
Steep Potential Well

Global Existence and Asymptotic Behavior of Solutions for Nonlinear Wave Equations

2014 ◽  
Vol 490-491 ◽  
pp. 327-330
Author(s):  
Ji Bing Zhang ◽  
Yun Zhu Gao
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Nonlinear Wave Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Source Terms ◽  
Damping And Source Terms

In this paper, we concern with the nonlinear wave equations with nonlinear damping and source terms. By using the potential well method, we obtain a result for the global existence and asymptotic behavior of the solutions.

scholarly journals Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun Ye
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equations ◽  
Decay Estimate ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Initial Boundary Value ◽  
Nonlinear Degenerate

This paper studies the existence of global solutions to the initial-boundary value problem for some nonlinear degenerate wave equations by means of compactness method and the potential well idea. Meanwhile, we investigate the decay estimate of the energy of the global solutions to this problem by using a difference inequality.

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→∞.

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