scholarly journals Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

2021 ◽  
Vol 26 (4) ◽  
pp. 626-641
Author(s):  
Jiafa Xu ◽  
Jie Liu ◽  
Donal O'Regan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
High Energy ◽  
Nonlinear Schrodinger Equation ◽  
Infinitely Many Solutions ◽  
Fountain Theorem ◽  
Nonlinear Schrödinger ◽  
Cerami Condition

In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for the equation.

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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