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
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.

We study the existence of spatial periodic solutions for nonlinear elliptic equations $-\Delta u\phantom{\rule{0.166667em}{0ex}}+\phantom{\rule{0.166667em}{0ex}}g(x,u\left(x\right))=0,\phantom{\rule{0.277778em}{0ex}}x\in {\mathbb{R}}^{N}$ where $g$ is a continuous function, nondecreasing w.r.t. $u$. We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions $g$ are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations....

We study the existence of spatial periodic solutions for nonlinear
elliptic equations $-\Delta u\phantom{\rule{0.166667em}{0ex}}+\phantom{\rule{0.166667em}{0ex}}g(x,u\left(x\right))=0,\phantom{\rule{0.277778em}{0ex}}x\in {\mathbb{R}}^{N}$
where is a continuous function, nondecreasing w.r.t. . We
give necessary and sufficient conditions for the existence of
periodic solutions. Some cases with nonincreasing functions
are investigated as well. As an application we analyze the
mathematical model of electron beam focusing system and we prove
the existence of positive periodic solutions for the envelope
equation. We present also numerical simulations.
...

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