We consider the existence of infinitely many solutions to the boundary value problem $$\begin{array}{c}\frac{\mathrm{d}}{\mathrm{d}t}\left({\frac{1}{2}}_0{D}_t^{-\beta }\left(u^{\text{'}}\left(t\right)\right)+{\frac{1}{2}}_t{D}_T^{-\beta }\left(u^{\text{'}}\left(t\right)\right)\right)+\nabla F(t,u\left(t\right))=0\text{a.e.}t\in [0,T],\\ u\left(0\right)=u\left(T\right)=0.\end{array}$$ Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.

The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.

The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.