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On the spectrum of perturbed differential operators with periodic coefficients. (Russian)
Authors: Kozhukhari P. A.
$$
H=\sum^n_{k=0}h_k(t)\left(\frac d{dt}\right)^{n-k},
$$
where $h_k(t)=a_k(t)+b_k(t)$; $a_k(t)$ ($k=0,1,\dots, n; \ a_0(t)\ne 0$) -- are functions of period $T$;
$b_k(t)$ ($k=0,1,\dots, n; \ b_0(t)\ne 0$) -- are measurable functions (in general complex). Operator is acting in Banach space $L_p(0,\infty)$ ($1\le p<\infty$) \ (the choice of boundary conditions is not important). The obtained results are true for differential operator with matrix coefficients.
Abstract
Some conditions are established, which quarante the absence of eigenvalues for the differential operator$$
H=\sum^n_{k=0}h_k(t)\left(\frac d{dt}\right)^{n-k},
$$
where $h_k(t)=a_k(t)+b_k(t)$; $a_k(t)$ ($k=0,1,\dots, n; \ a_0(t)\ne 0$) -- are functions of period $T$;
$b_k(t)$ ($k=0,1,\dots, n; \ b_0(t)\ne 0$) -- are measurable functions (in general complex). Operator is acting in Banach space $L_p(0,\infty)$ ($1\le p<\infty$) \ (the choice of boundary conditions is not important). The obtained results are true for differential operator with matrix coefficients.
Contents
- Countably compact topologies on Boolean rings. (Russian)
- Locally dissipative dynamical systems and some of their applications. (Russian)
- Conditions for the maximal multiplicity of an integral line of a differential system with homogeneities of $m$th order. (Russian)
- On the spectrum in the right half-plane of a class of operator pencils. (Russian)
- K-loops. (Russian)
- Groups of automorphisms of medial quasigroups and medial fields. (Russian)
- On the spectrum of perturbed differential operators with periodic coefficients. (Russian)
- Parametric completeness in the logic of the simplest pseudo-Boolean algebra with incomparable elements. (Russian)
- Coefficient conditions for the coexistence of two singular points of summed multiplicity 4 in a finite part of a phase plane of a quadratic system. (Russian)
- On the kinds of two-dimensional multiregular partitions. (Russian)
- On a class of nonlocal generalized splines. (Russian)
- On the number of near neighbors in regular partitions of Lobachevskij space by compact polyhedra. (Russian)
- An approximation algorithm for matroids with coalitions. (English)
- On finite projection of nonstationary $M/GI/1$ queueing systems. (English)
- Numerical modeling of the process of high-velocity penetration of an obstacle. (Russian)
