Generalized solvability of the classical boundary value problems for analytic and quasiconformal functions in arbitrary Jordan domains with boundary data that are measurable with respect to the logarithmic capacity is ...
We proved a theorem about the integral of quaternionic-differentiable functions of spatial variable over the closed surface. It is an analog of the Cauchy theorem from complex analysis.
We consider the dynamics of solutions for autonomous reaction-diffusion equation in Rⁿ with multivalued nonlinearity. The a priory estimates for solutions are obtained. The existence of compact invariant global attractor ...
A new class of global mixed Abelian groups, called W-groups, is defined. The following isomorphism theorem for commutative modular group algebras of such groups is proved: If G is a p-mixed μ-elementary W-group for some ...
This paper is concerned with elliptic problems including a small parameter multiplying higher order derivatives. We found algebraic conditions on the operator and boundary conditions which guarantee the Fredholm property, ...
In present work, we continue the study the growth of the orthogonal polynomials over a contour with weight function in the weighted Lebesgue space, when the contour and the weight function having some singularities. We ...
The notions of a pencil of the second order and a linear fractional relation (LFR) are defined in spaces of linear bounded operators acting between Banach spaces. It is shown that these notions are closely connected with ...
A new approach to the approximate solution of Fredholm integral equations of the first kind with finitely smoothing operators is worked out. It is established that on wide classes of such equations this approach allows to ...
В этой статье рассмотрена обратная краевая задача для псевдопараболического уравнения третьего порядка с интегральным условием. Сначала исходная задача сводится к эквивалентной (в определённом смысле) задаче, для которой ...
We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where L : Cⁿ → Rⁿ₊ is a continuous positive vector-function. They give an estimate of the maximum ...
The solvability of the Cauchy problem u(0) = u₀ of an semilinear differential operator equation Lǔ = Mu+N(u) is under consideration. The abstract results are illustrated by the Cauchy–Dirichlet problem for degenerate ...
We study the existence and nonexistence of positive (super) solutions to a singular quasilinear second-order elliptic equations with structural coefficients from non-linear Kato-type classes. Under certain general assumptions ...
Power Geometry (PG) is a new calculus developing the differential calculus and aimed at nonlinear problems. The main concept of PG is the study of nonlinear problems in logarithms of original coordinates. Then many relations ...
It is proved criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between domains on the Riemann surfaces by prime ends of Caratheodory.
In this paper we start to investigate a new notion of pseudo-nearrings and a generalization of linear spaces to quasi-modules over pseudo-nearrings. Pseudo-nearrings can be treated as ringoids in the sense of J. Hion (see ...
We consider first-order symmetric system Jy′ −A(t)y = λ∆(t)y with n×n-matrix coefficients defined on an interval [a, b) with the regular endpoint a. It is assumed that the deficiency indices N± of the system satisfies N− ...