scholarly journals Fixed energy problem for nonlinear Schrödinger operator

2018 ◽  
Vol 1141 ◽  
pp. 012112
Author(s):  
Valery Serov
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Energy Problem ◽  
Nonlinear Schrödinger ◽  
Fixed Energy ◽  
Nonlinear Schrödinger Operator

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.

Inverse scattering for the higher order Schrödinger operator with a first order perturbation

2019 ◽  
Vol 27 (3) ◽  
pp. 409-427
Author(s):  
Hua Huang ◽  
Zhiwen Duan ◽  
Quan Zheng
Keyword(s):  
Inverse Scattering ◽  
Schrödinger Operator ◽  
Scattering Matrix ◽  
Higher Order ◽  
Zero Order ◽  
Schrodinger Operator ◽  
Scattering Problems ◽  
First Order ◽  
Fixed Energy ◽  
First Order Perturbation

Abstract This paper concerns inverse scattering problems at a fixed energy for the higher order Schrödinger operator with the first order perturbed potentials in dimensions {n\geq 3} . We show that the scattering matrix uniquely determines the first order perturbed potentials and the zero order potentials.

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