Nonlinear Oscillations

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On the structure of the set of continuously differentiable solutions of one boundary-value problem for a system of functional differential equations of neutral type
Nonlinear Oscillations - Tập 10 - Trang 278-291 - 2007
H. P. Pelyukh, A. V. Vel’hach
We study the structure of the set of solutions, continuously differentiable for t ∈ R + = [0; + ∞), of one limit problem for systems of nonlinear functional differential equations of neutral type with nonlinear deviations of argument that depend on an unknown function.
Invariant Sets of Systems of Stochastic Differential Equations with Jumps
Nonlinear Oscillations - Tập 8 - Trang 233-239 - 2005
H. L. Kulinich, S. V. Kushnirenko
We introduce the notion of invariant surfaces for inhomogeneous stochastic differential equations with jumps. The results obtained enable one to determine invariant surfaces for stochastic differential equations of the type indicated.
On the minimal speed of traveling waves for a nonlocal delayed reaction–diffusion equation
Nonlinear Oscillations - Tập 13 - Trang 1-9 - 2010
M. Aguerrea, G. Valenzuela
In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for a nonlocal delayed reaction–diffusion equation.
On Goursat and Dirichlet problems for one equation of the third order
Nonlinear Oscillations - Tập 11 - Trang 320-330 - 2009
T. D. Dzhuraev, O. S. Zikirov
We study the problem of the unique solvability of Goursat and Dirichlet problems for one partial differential equation of the third order. We construct a Riemann function for a linear third-order equation with a hyperbolic operator in the principal part, study some properties of the Riemann function, and then use them to prove theorems on the existence and uniqueness of a solution of the problems ...... hiện toàn bộ
Systems of nonlinear differential equations with bounded solutions
Nonlinear Oscillations - Tập 11 - Trang 168-176 - 2008
I. M. Hrod
We establish sufficient conditions for the existence of solutions bounded on ℝ for the equation {fx168-01}, in a finite-dimensional Banach space {ie168-01}.
Boundary-value problems for linear equations with a generalized invertible operator in a Banach space with basis
Nonlinear Oscillations - Tập 13 - Trang 558-568 - 2011
V. F. Zhuravlev
We consider linear boundary-value problems for operator equations with generalized invertible operators in Banach spaces that have bases. Using the technique of generalized inverse operators applied to generalized invertible operators in Banach spaces, we establish conditions for the solvability of linear boundary-value problems for these operator equations and obtain formulas for the representati...... hiện toàn bộ
On Sufficient Conditions for the Convergence of a Modified Collocation–Iterative Method for the Solution of Nonlinear Equations
Nonlinear Oscillations - Tập 5 - Trang 60-70 - 2002
V. B. Poselyuzhna
We consider the problem of application of the collocation–iterative method to the solution of nonlinear integral equations. We construct an algorithm of the method and establish sufficient conditions for the convergence of the method.
Investigation of the structure of the set of continuous solutions of systems of linear functional difference equations
Nonlinear Oscillations - Tập 12 - Trang 314-345 - 2010
H. P. Pelyukh, O. A. Sivak
We establish conditions for the existence of continuous solutions of systems of linear functional difference equations with linearly transformed argument and develop a method for the construction of these solutions.
Construction of asymptotic solutions of a singularly perturbed linear system of differential equations with irregular singular point in the case of a multiple spectrum of the boundary matrix
Nonlinear Oscillations - Tập 11 - Trang 135-151 - 2008
V. P. Yakovets’, O. V. Holovchenko
We construct asymptotic solutions of a singularly perturbed linear system of differential equations with irregular singular point. We consider the case where the main matrix has a multiple eigenvalue associated with one or several elementary divisors of the same multiplicity. We establish that, in the case of multiple elementary divisors, the corresponding asymptotic expansions can be constructed ...... hiện toàn bộ
Canonical reduction on cotangent symplectic manifolds with group action and on associated principal fiber bundles with connection
Nonlinear Oscillations - Tập 9 - Trang 96-106 - 2006
Ya. A. Prykarpats’kyi
We study properties of the canonical reduction method on cotangent symplectic manifolds with group action. We demonstrate a deep inner relationship between reduced symplectic structures and canonical connections on associated principal fiber bundles.
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