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Similar Journals
 Nonlinear OscillationsNumber of Followers: 1      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1536-0059 - ISSN (Online) 1536-0059 Published by Springer-Verlag  [2626 journals]
• Nonexistence of a global solution of a mixed problem for a nonlinear
system of equations with integral perturbation in a domain unbounded with
respect to time variable
• Authors: H. R. Bazylyak; M. O. Nechepurenko
Pages: 461 - 471
Abstract: We study a mixed problem for a nonlinear connected evolution system of equations with integral perturbation in a domain unbounded with respect to the time variable. We prove that a global generalized solution of this problem does not exist.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0170-8
Issue No: Vol. 14, No. 4 (2012)

• On stability of solutions of nonlinear nonstationary systems of impulsive
differential equations in a critical case
• Authors: A. I. Dvirnyi; V. I. Slyn’ko
Pages: 472 - 496
Abstract: We study the problem of stability of critical equilibrium states for a nonlinear system of impulsive differential equations in a special case. The investigation is carried out on the basis of direct Lyapunov method with the use of two auxiliary functions.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0171-7
Issue No: Vol. 14, No. 4 (2012)

• Asymptotic behavior of one class of solutions of nonlinear nonautonomous
second-order differential equations
• Authors: A. A. Koz’ma
Pages: 497 - 511
Abstract: For a second-order ordinary differential equation whose right-hand side contains a sum of terms with nonlinearities regularly varying with respect to the unknown function and its derivatives, we establish necessary and sufficient conditions for the existence of a broad class of monotone solutions and obtain exact asymptotic representations of solutions of this class in a neighborhood of a singular point.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0172-6
Issue No: Vol. 14, No. 4 (2012)

• Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright
circular cylindrical tank. I. Modal equations
• Authors: I. Lukovsky; D. Ovchynnykov; A. Timokha
Pages: 512 - 525
Abstract: Combining the Lukovsky–Miles variational method and the Narimanov–Moiseev asymptotics, we deduce a nonlinear modal system describing the resonant liquid sloshing in an upright circular cylindrical tank. The sloshing occurs due to a small-amplitude periodic or an almost-periodic excitation with forcing frequency close to the lowest natural sloshing frequency. In contrast to the existing nonlinear modal systems based on the Narimanov–Moiseev asymptotic intermodal relations, the derived modal equations (i) contain all necessary (infinitely many) generalized coordinates of the second and third orders and (ii) include exclusively nonzero hydrodynamic coefficients, for which (iii) fairly simple computational formulas are found. As a consequence, the modal equations can be used in analytical studies of nonlinear sloshing phenomena, which will be demonstrated in the forthcoming Part II.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0173-5
Issue No: Vol. 14, No. 4 (2012)

• Iterative method for quasilinear integral equations with constraints
• Authors: A. Yu. Luchka; V. F. Mel’nychuk
Pages: 526 - 536
Abstract: We establish conditions for the existence of solutions of quasilinear integral equations with quasilinear constraints and substantiate the applicability of the iterative method to these equations.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0174-4
Issue No: Vol. 14, No. 4 (2012)

• Almost periodic solutions of Mackey–Glass equations with pulse
action
• Authors: Yu. M. Myslo; V. I. Tkachenko
Pages: 537 - 546
Abstract: We obtain conditions for the permanence and existence of a positive, asymptotically stable, piecewisecontinuous, almost periodic solution of the Mackey–Glass equation with almost periodic coefficients and pulse action.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0175-3
Issue No: Vol. 14, No. 4 (2012)

• Averaging of fuzzy differential equations on a finite interval
• Authors: A. V. Plotnikov; T. A. Komleva
Pages: 547 - 559
Abstract: We substantiate the applicability of total and partial averaging schemes to the investigation of systems of fuzzy differential equations with a small parameter.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0176-2
Issue No: Vol. 14, No. 4 (2012)

• Quasisolutions of fuzzy differential inclusions
• Authors: N. V. Skripnik
Pages: 560 - 567
Abstract: We introduce the notion of a quasisolution of a fuzzy differential inclusion and study the relationship between the sets of ordinary solutions and quasisolutions.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0177-1
Issue No: Vol. 14, No. 4 (2012)

• Exponentially dichotomous difference equations with non-Lipschitz
perturbations
• Authors: V. Yu. Slyusarchuk
Pages: 568 - 588
Abstract: We establish conditions for the existence of bounded solutions of nonlinear difference equations.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0178-0
Issue No: Vol. 14, No. 4 (2012)

• On one delay dynamical model in economics
• Authors: D. Ya. Khusainov; J. Diblík; M. Růžičková; A. Baštincová
Pages: 589 - 601
Abstract: We consider the Leont’ev dynamical model described by a system of delay differential equations. The stability of a program solution is studied by the method of Lyapunov functions with Razumikhin condition. We obtain an estimate for the convergence of solutions of the system to the program solution.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0179-z
Issue No: Vol. 14, No. 4 (2012)

• Periodic solutions of degenerate linear systems of differential equations
• Authors: A. A. Chechel’
Pages: 602 - 606
Abstract: We propose a method for finding periodic solutions of degenerate linear systems of differential equations in the case where the zero eigenvalues of the matrix coefficients of the derivatives are simple. We also consider the solution of boundary-value problems for such systems.
PubDate: 2012-04-01
DOI: 10.1007/s11072-012-0180-6
Issue No: Vol. 14, No. 4 (2012)

• Periodic solutions of systems of linear difference equations with
continuous argument
• Authors: N. A. Bohai
Pages: 305 - 312
Abstract: We establish conditions for the existence of continuous periodic solutions of systems of linear difference equations and develop a method for their construction.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0159-3
Issue No: Vol. 14, No. 3 (2012)

• Asymptotic behavior of solutions of nonlinear cyclic systems of ordinary
differential equations
Pages: 313 - 333
Abstract: We obtain asymptotic representations for one class of solutions of cyclic nonlinear systems of ordinary differential equations of more general type than the Emden–Fowler systems.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0160-x
Issue No: Vol. 14, No. 3 (2012)

• Application of the averaging method to the investigation of stability of
difference-differential equations
• Authors: I. I. Klevchuk
Pages: 334 - 341
Abstract: We use the second approximation of the averaging method for the investigation of stability of a system of weakly coupled oscillators with delay. A sufficient condition for the stability (instability) of a linear system of difference-differential equations is obtained.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0161-9
Issue No: Vol. 14, No. 3 (2012)

• Averaging in fuzzy controlled systems
• Authors: T. A. Komleva; L. I. Plotnikova; A. V. Plotnikov; N. V. Skripnik
Pages: 342 - 349
Abstract: We consider the applicability of the scheme of complete averaging to control problems with terminal quality criterion in the case where the behavior of the system is described by a controlled fuzzy differential equation.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0162-8
Issue No: Vol. 14, No. 3 (2012)

• Asymptotic representations of solutions of one class of nonlinear
differential equations of the second order
• Authors: L. I. Kusik
Pages: 350 - 368
Abstract: We establish asymptotic properties of some types of solutions of one class of essentially nonlinear nonautonomous differential equations of the second order and find necessary and sufficient conditions for the existence of these solutions.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0163-7
Issue No: Vol. 14, No. 3 (2012)

• Stabilization of optically coupled lasers with periodic pumping
• Authors: P. J. Torres
Pages: 414 - 422
Abstract: We study a periodically forced system modeling the synchronization of two optically coupled lasers pumped by an alternating current. A necessary and sufficient condition for the existence of a periodic solution is given, as well as a sufficient condition for its uniqueness and asymptotic stability.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0166-4
Issue No: Vol. 14, No. 3 (2012)

• On some examples in the theory of abstract Cauchy problems
• Authors: A. V. Chaikovs’kyi
Pages: 423 - 431
Abstract: We give examples of abstract Cauchy problems proving that inclusions in a chain of functional classes are strict and disproving a sufficient condition for the solvability of the Cauchy problem published earlier.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0167-3
Issue No: Vol. 14, No. 3 (2012)

• Convergence of the positive solutions of a nonlinear neutral difference
equation
• Authors: G. E. Chatzarakis; G. L. Karakostas; I. P. Stavroulakis
Pages: 432 - 444
Abstract: Sufficient conditions are established that guarantee the convergence of the positive solutions of a neutral-type difference equation of the form $$\Delta [x(n) - q(n)x(\sigma (n))] + p(n)f(x({\tau_1}(n)), \ldots, x({\tau_k}(n))) = 0,$$ where σ(n); n = 1, 2, …, are retarded arguments and τ j (n) j = 1, …, k, are general deviated arguments.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0168-2
Issue No: Vol. 14, No. 3 (2012)

• On approximate solution of periodic boundary-value problems with delay by
the least-squares method in the critical case
• Authors: S. M. Chuiko; A. S. Chuiko
Pages: 445 - 460
Abstract: We establish necessary and sufficient conditions for the existence of solutions of a weakly nonlinear Noether boundary-value problem for a system of ordinary delay differential equations in the critical case.
PubDate: 2012-01-01
DOI: 10.1007/s11072-012-0169-1
Issue No: Vol. 14, No. 3 (2012)

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