卷 215, 编号 3 (2016)
- 年: 2016
- 文章: 12
- URL: https://journals.rcsi.science/1072-3374/issue/view/14740
Article
Continuous Solutions of Systems of Nonlinear Difference Equations
摘要
We establish sufficient conditions for the existence of continuous solutions of one class of systems of nonlinear difference equations.
Well-Posedness of Dirichlet and Poincaré Problems in a Cylindrical Domain for Degenerate Multidimensional Hyperbolic Equations with Gellerstedt Operator
摘要
We prove that the Dirichlet and Poincar´e problems for degenerate multidimensional hyperbolic equations with Gellerstedt operator in a cylindrical domain are uniquely solvable and establish a criterion of uniqueness for the regular solutions of these problems.
Investigation of Stability in the Case of Neutral Linear Approximation
摘要
We study the problem of stability in the case of neutral linear approximation.
Asymptotics of the Solutions of Second-Order Differential Equations with Rapidly Varying Nonlinearity
摘要
We establish asymptotic representations for one class of solutions of a second-order differential equation of the Emden–Fowler type with rapidly varying nonlinearity.
Periodic Solutions of a System of Linear Inhomogeneous Differential Equations of the First Order with Rectangular Periodic Matrices
摘要
We establish sufficient conditions for the reduction of a system of linear inhomogeneous differential equations of the first order with rectangular periodic matrices to a canonical from and construct the general periodic solution of this system.
Singularity of the Digit Inversor for the Q3-Representation of the Fractional Part of a Real Number, Its Fractal and Integral Properties
摘要
We introduce and study a continuous function I which is called a digit inversor for the Q3-representation of the fractional part of a real number. This representation is determined by a probability vector.(q0; q1; q2) with positive coordinates, generalizes the classical ternary representation, and coincides with this representation for q0 = q1 = q2 = 1/3: The values of this function are obtained from the Q3-representation of the argument by the following change of digits: 0 by 2; 1 by 1; and 2 by 0: The differential, integral, and fractal properties of the inversor are described. We prove that I is a singular function for q0 ≠ q2.
Existence of Countably Many Cycles in Hyperbolic Systems of Differential Equations with Transformed Argument
摘要
We prove the existence of countably many periodic solutions of a hyperbolic system of first-order differential equations with periodic condition. The problems of existence and stability of traveling waves are investigated for a quasilinear Korteweg–de Vries equation with transformed argument and for the equation of spin combustion.
Asymptotic Analysis of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations
摘要
We consider a homogeneous system of linear singularly perturbed differential equations of order m with matrix at higher derivatives that becomes singular as the small parameter approaches zero. By using the Newton diagrams, we study the structure of the general solution of the analyzed system and the possibility of construction of its asymptotics in the case where the corresponding characteristic polynomial of the matrix has multiple finite and infinite elementary divisors. The obtained results generalize the results obtained for similar systems of equations of the first and second orders.
The Fixed-Point Property Under Induced Interval Maps of Continua
摘要
Let f : I → I be a continuous map of a compact interval I and let C(I) be hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We study the fixed-point property of the subsets of C (I) with respect to any induced interval map ℱ : C (I) → C (I). In particular, we prove that any nonempty subcontinuum of C (I) possesses the fixed-point property.
Periodic and Almost Periodic Solutions of Difference Equations in Metric Spaces
摘要
We establish conditions for the existence of almost periodic and periodic solutions of almost periodic difference equations with discrete argument in a metric space without using the -classes of these equations.
Determination of the Frequencies and Modes of Natural Oscillations of Liquids in Composed Vessels
摘要
We develop a variation method for the solution of the spectral problems for free oscillations of liquids in axially symmetric vessels of complex geometry. The problem is formulated in terms of the conjugation method. We obtain a generalized functional for which the conjugation conditions on the adjacent parts of the introduced subdomains are natural boundary-value conditions. We use the Trefts method for the reduction of the original problem to a problem of solution of an algebraic problem of low dimension. The results of calculations confirm the efficiency of the proposed method.
Asymptotic Representations for the Solutions of Third-Order Nonlinear Differential Equations
摘要
We study the asymptotic behavior of solutions for a certain class of third-order nonlinear nonautonomous differential equations.