scholarly journals On the essential spectrum of the many-particle Schrödinger operator with combined Zeeman and Stark effect

1967 ◽  
Vol 3 (3) ◽  
pp. 271-287 ◽  
Author(s):  
Masaharu Arai
Keyword(s):  
Essential Spectrum ◽  
Schrödinger Operator ◽  
Stark Effect ◽  
Schrodinger Operator ◽  
The Many

scholarly journals A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Shaowei Chen ◽  
Haijun Zhou
Keyword(s):  
Schrödinger Equation ◽  
Essential Spectrum ◽  
Nonlinear Schrödinger Equation ◽  
Schrödinger Operator ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Infinitely Many Solutions ◽  
Schrodinger Operator ◽  
Nonlinear Schrödinger ◽  
Negative Eigenvalues

We consider the nonlinear Schrödinger equation-Δu+f(u)=V(x)u  in  RN. The potential functionVsatisfies that the essential spectrum of the Schrödinger operator-Δ-Vis[0,+∞)and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearityfsatisfies the resonance type conditionlimt→∞f(t)/t=0. Under some additional conditions onVandf, we prove that this equation has infinitely many solutions.

scholarly journals The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum

2021 ◽  
Vol 2070 (1) ◽  
pp. 012017
Author(s):  
J.I. Abdullaev ◽  
A.M. Khalkhuzhaev
Keyword(s):  
Essential Spectrum ◽  
Schrödinger Operator ◽  
Three Dimensional ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
Dimensional Lattice ◽  
Pairwise Potential ◽  
Zero Range

Abstract We consider a three-particle discrete Schrödinger operator Hμγ (K), K 2 T3 associated to a system of three particles (two fermions and one different particle) interacting through zero range pairwise potential μ > 0 on the three-dimensional lattice Z 3. It is proved that the operator Hμγ (K), ||K|| < δ, for γ > γ0 has at least two eigenvalues in the gap of the essential spectrum for sufficiently large μ > 0.

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