[Author]
 Dorodnyi, M. A.

[Title]
 Homogenization of the periodic Schr\"{o}dinger-type equations with the lower
 order terms

[AMS Subj-class]
 35B27 Homogenization; equations in media with periodic structure

[Keywords]
 Periodic differential operators, Nonstationary Schr\"{o}dinger-type equations,
 Homogenization, Effective operator, Operator error estimates

[Abstract]
 In $L_2 (\mathbb{R}^d; \mathbb{C}^n)$, we consider a selfadjoint matrix strongly
 elliptic second order differential operator $\mathcal{B}_\varepsilon$,
 $0<\varepsilon \le 1$, with periodic coeffcients depending on
 $\mathbf{x}/\varepsilon$. The principal part of this operator is given in a
 factorized form, the operator involves lower order terms. We find approximations
 of the exponential $e^{-is \mathcal{B}_\varepsilon}$, $s \in \mathbb{R}$, for
 small $\varepsilon$ in the ($H^r \to L_2$)-operator norm with suitable $r$.
 The results are applied to study the behavior of the solution
 $\mathbf{u}_\varepsilon$ of the Cauchy problem for the Schr\"{o}dinger-type
 equation $i\partial_{s} \mathbf{u}_\varepsilon = \mathcal{B}_\varepsilon
 \mathbf{u}_\varepsilon + \mathbf{F}$. Applications to the magnetic
 Schr\"{o}dinger equation with a singular electric potential and the
 two-dimensional Pauli equation with singular potentials are given.

[Comments]
 LaTeX, Russian, 69 pp.

[Contact e-mail]
 mdorodni@yandex.ru