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Том 212, № 3 (2016)
- Год: 2016
- Статей: 10
- URL: https://ogarev-online.ru/1072-3374/issue/view/14707
Article
Multipoint Problem for a System of Hyperbolic Equations with Mixed Derivative
Аннотация
We consider a multipoint problem with data lying on the characteristics of a system of hyperbolic equations of the second order with two independent variables. We introduce new unknown functions and reduce the problem to an equivalent problem formed by a family of multipoint problems for systems of ordinary differential equations and functional relations. We establish conditions for the existence of a unique solution in terms of the coefficients of multipoint problems.
213-233
234-253
Properties of Continuous Periodic Solutions of Systems of Functional-Differential Equations with Small Parameter
Аннотация
We establish sufficient conditions for the existence of periodic solutions of a system of nonlinear functional-differential equations with small parameter and linear deviations of the argument and study the properties of these solutions.
254-263
264-274
Generalized Inversion of Fredholm Integral Operators with Degenerate Kernels in Banach Spaces
Аннотация
We establish conditions required for the generalized invertibility of Fredholm integral operators with degenerate kernels in Banach spaces. New results on the generalized inversion of Fredholm integral operators with degenerate kernels in Banach spaces are obtained. A detailed analysis of an example is also presented.
275-289
290-304
Asymptotics of the General Solution of Linear Singularly Perturbed Systems of Higher-Order Differential Equations with Degeneration in the Case of Multiple Spectrum of the Limiting Matrix Pencil
Аннотация
We construct an asymptotic expansion for the fundamental system of solutions of a linear singularly perturbed system of m-order differential equations with degenerate principal matrix at the higher-order derivatives. The case where the corresponding characteristic polynomial has a multiple spectrum is investigated. It is proved that, in this case, the asymptotic expansions are constructed in the fractional powers of the small parameter. The recurrence formulas for the coefficients of these expansions are obtained.
305-325
326-334
Almost Periodic Solutions of Nonlinear Discrete Systems that Can Be Not Almost Periodic in Bochner’s Sense
Аннотация
We introduce a new class of almost periodic operators and establish the conditions of existence of almost periodic solutions of nonlinear discrete equations. These solutions can be not almost periodic in Bochner’s sense.
335-348
Additional Reductions in the K -Constrained Modified KP Hierarchy
Аннотация
Additional reductions are proposed for the modified k-constrained KP hierarchy. As a result, we obtain generalizations of Kaup–Broer system, Korteweg–de-Vries equation, and a modification of the Korteweg–de-Vries equation that belongs to the modified k-constrained KP hierarchy. We also propose a solution generating technique based on binary Darboux transformations for the obtained equations.
349-369