On the essential spectrum of electromagnetic Schrödinger operator with singular electric potential

2012 ◽  
Vol 59 (1) ◽  
pp. 18-27 ◽  
Author(s):  
A.R. Aliev ◽  
E.H. Eyvazov
Keyword(s):  
Essential Spectrum ◽  
Schrödinger Operator ◽  
Electric Potential ◽  
Schrodinger 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.

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