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Volume 238, Nº 3 (2019)

Article

One Approach to the Solution of a Nonlocal Problem for Systems of Hyperbolic Equations with Integral Conditions

Asanova A.

Resumo

We consider a nonlocal problem with integral conditions for a system of hyperbolic equations with two independent variables. We study the solvability of the considered problem and construct algorithms aimed at finding its approximate solutions by introducing additional functional parameters. The investigated problem is reduced to an equivalent problem that consists of the Goursat problem for a system of hyperbolic equations with parameters and a boundary-value problem with integral condition for a system of ordinary differential equations for the introduced parameters. We propose algorithms for finding approximate solutions of the problem based on the algorithms used for the solution of the equivalent problem and prove their convergence to the exact solution.

Journal of Mathematical Sciences. 2019;238(3):189-206
pages 189-206 views

Nonclassical Symmetries of a System of Nonlinear Reaction-Diffusion Equations

Barannyk T.

Resumo

We study the conditional symmetry of a system of nonlinear reaction-diffusion equations and establish the existence of operators of conditional symmetry for systems of nonlinear reaction-diffusion equations with any number of independent variables and find these operators in the explicit form. The exact solutions of nonlinear reaction-diffusion equations with exponential nonlinearity are constructed.

Journal of Mathematical Sciences. 2019;238(3):207-214
pages 207-214 views

Asymptotic Bounds for the Solutions of a Functional-Differential Equation with Linearly Transformed Argument

Bel’skii D., Pelyukh G.

Resumo

We establish new properties of solutions of a functional-differential equation with linearly transformed argument.

Journal of Mathematical Sciences. 2019;238(3):215-223
pages 215-223 views

Bifurcation of Solutions of the Boundary-Value Problem for Systems of Integrodifferential Equations with Degenerate Kernel

Bondar I., Ovchar R.

Resumo

We establish sufficient conditions for the existence of solutions of a weakly perturbed linear boundary-value problems for a system of integrodifferential equations. We also establish conditions for the existence and uniqueness of solutions of problems of this kind and propose an iterative procedure for the construction of the required solutions.

Journal of Mathematical Sciences. 2019;238(3):224-235
pages 224-235 views

Synchronization Analysis for a Class of Genetic Oscillator Networks

Gao Q., Du J., Liu X.

Resumo

We consider a synchronization problem for genetic oscillator networks. The genetic oscillators are modeled as nonlinear systems of the Lur’e type. Simple and verifiable synchronization conditions are presented for genetic oscillator networks by using the theory of absolute stability and the matrix theory. A network composed of coupled Goodwin models is used as an example of numerical simulation to verify the efficiency of the theoretical method.

Journal of Mathematical Sciences. 2019;238(3):236-247
pages 236-247 views

Weakly Perturbed Boundary-Value Problems for the Fredholm Integral Equations with Degenerate Kernel in Banach Spaces

Zhuravlev V., Fomin N.

Resumo

We consider weakly perturbed boundary-value problems for the Fredholm integral equations with degenerate kernel in Banach spaces and establish the conditions of bifurcation from the point ε = 0 for the solutions of weakly perturbed boundary-value problems for Fredholm integral equations with degenerate kernel in Banach spaces. A convergent iterative procedure is proposed for finding the solutions in the form of series \( {\sum}_{i=-1}^{+\infty }{\varepsilon}^i{z}_i(t) \) in powers of ε.

Journal of Mathematical Sciences. 2019;238(3):248-262
pages 248-262 views

On the Exponential Stability of a Trivial Torus for One Class of Nonlinear Impulsive Systems

Kapustyan O., Asrorov F., Perestyuk Y.

Resumo

We prove the exponential stability of a trivial torus for a class of nonlinear extensions of dynamical systems on a torus. The obtained results can be applied to the study of stability of toroidal sets for a certain class of impulsive dynamical systems.

Journal of Mathematical Sciences. 2019;238(3):263-270
pages 263-270 views

Asymptotic Expansion of the Solution of a Linear Parabolic Boundary-Value Problem in a Thin Starlike Joint

Klevtsovs’kyi A.

Resumo

We consider a linear parabolic boundary-value problem in a thin 3D starlike joint that consists of a finite number of thin curvilinear cylinders connected through a domain (node) with diameter O(ε). We develop a procedure for the construction of the complete asymptotic expansion of the solution as ε → 0, i.e., in the case where the starlike joint is transformed into a graph. By using the method of matching of the asymptotic series, we deduce the limit problem (ε = 0) on a graph with the corresponding Kirchhoff-type conjugation conditions at the vertex. We also prove asymptotic estimates, which enable us to trace the influence of the geometric shape of the node and the physical processes running in the node on the global asymptotic behavior of the solution.

Journal of Mathematical Sciences. 2019;238(3):271-291
pages 271-291 views

Averaging Scheme for Integrodifferential Inclusions

Komleva T., Plotnikov A.

Resumo

We substantiate an averaging scheme for integrodifferential inclusions on a bounded interval.

Journal of Mathematical Sciences. 2019;238(3):292-301
pages 292-301 views

Fixed-Point Theorems and Difference Equations with Nonempty Set of Bounded Solutions

Slyusarchuk V.

Resumo

We present new fixed-point theorems for mappings acting on a metric space and establish conditions for the existence of bounded solutions of difference equations.

Journal of Mathematical Sciences. 2019;238(3):302-315
pages 302-315 views

Asymptotic Representations for the Solutions of Second-Order Differential Equations with Rapidly and Regularly Varying Nonlinearities

Chepok O.

Resumo

We determine asymptotic representations for the solutions of one class of second-order differential equations with rapidly and regularly varying nonlinearities.

Journal of Mathematical Sciences. 2019;238(3):316-332
pages 316-332 views

Matrix Differential-Algebraic Boundary-Value Problem with Pulsed Action

Chuiko S., Dzyuba M.

Resumo

We establish necessary and sufficient conditions for the existence of solutions of a linear matrix boundaryvalue problem for a system of matrix differential-algebraic equations with pulsed action. We also construct a generalized Green operator of linear boundary conditions for a system of matrix differentialalgebraic equations with pulse action. To solve the matrix differential-algebraic boundary problem with pulsed action, we use the original conditions of solvability and the structure of the general solution of the linear matrix equation.

Journal of Mathematical Sciences. 2019;238(3):333-343
pages 333-343 views

Correction

Correction to: Two-Sided Semi-Local Smoothing Splines

Silaev D., Ingtem J., Filippov A.

Resumo

The second author’s name should read J. G. Ingtem

In the article metadata on SpringerLink, the email icon should appear after J. G. Ingtem.

Journal of Mathematical Sciences. 2019;238(3):344-344
pages 344-344 views