Открытый доступ
Доступ предоставлен
Только для подписчиков
Том 235, № 1 (2018)
- Год: 2018
- Статей: 10
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14967
Article
OUR CONGRATULATIONS !
1-1
On a Reduction of the Order in a Differential-Algebraic System
Аннотация
The conditions of solvability and the structure of a generalized Green operator of the Cauchy problem for a linear differential-algebraic system are found. The sufficient conditions of reducibility of a differential-algebraic equation to a sequence of systems joining differential and algebraic equations are constructed. An original classification and a single scheme of construction of the solutions of differentialalgebraic equations are proposed.
2-14
Rapidly varying solutions of a second-order differential equation with regularly and rapidly varying nonlinearities
Аннотация
For a second-order differential equation whose the right-hand side contains the sum of terms with regularly and rapidly varying nonlinearities, we establish the conditions of existence and asymptotic representations of rapidly varying solutions, as the argument tends to a singular point.
15-34
Widths of the classes \( {B}_{p,\theta}^{\varOmega } \) of periodic functions of many variables in the space B1,1
Аннотация
We have obtained the exact-by-order estimates of Kolmogorov, linear, and trigonometric widths of the classes \( {B}_{p,\theta}^{\varOmega } \) of periodic functions of many variables in the space B1,1 the norm in which is stronger than the L1-norm.
35-45
46-51
Logarithmic Asymptotics of a Class of Mappings
Аннотация
The asymptotic behavior of lower Q-homeomorphisms relative to a p-modulus in ℝn, n ≥ 2, at a point is studied. A number of logarithmic estimates for the lower limits under various conditions imposed on the function Q are obtained. Some applications of these results to the Orlicz–Sobolev classes \( {W}_{\mathrm{loc}}^{1,\varphi } \) in ℝn, n ≥ 3 under the Calderon-type condition imposed on the function φ and, in particular, to the Sobolev classes \( {W}_{\mathrm{loc}}^{1,p} \) for p > n – 1 are given. The example of a homeomorphism with finite distortion which shows the exactness of the found order of growth is constructed.
52-62
63-73
Extreme problem for partially nonoverlapping domains on a Riemann sphere
Аннотация
The results of this work are referred to the well-known trend of the geometric theory of functions of complex variable, namely, to the extreme problems on the classes of nonoverlapping domains. It was started by Lavrent’ev’s classical work [1], where, in particular, the problem of the product of conformal radii of two nonoverlapping domains was first solved. Now, this trend is intensively developed. The main results can be found in [2–8] and [9–13]. Our results present a generalization of some results in [7].
74-80
Improved integrability and boundedness of solutions to some high-order variational problems
Аннотация
We give a series of results on the improved integrability and boundedness of solutions to several high-order variational problems with strengthened coercivity. In particular, we consider the homogeneous Dirichlet problem on the minimum of integral functionals and study variational inequalities with unilateral and bilateral obstacles and with integral and gradient constraints.
81-102
Approximative characteristics of functions from the classes \( {S}_{p,\theta}^{\varOmega } \)B(ℝd) with a given majorant of mixed moduli of continuity
Аннотация
We obtain the exact-by-order estimates of the approximation of functions from the classes \( {S}_{p,\theta}^{\varOmega } \)B(ℝd) in the space Lq(ℝd), 1 < p < q < ∞, by entire functions of the exponential type with supports of their Fourier transforms in sets generated by the level surfaces of a function Ω.
103-115