We study a system of linear singularly perturbed functional differential equations by the method
of integral manifolds. We construct a change of variables that decomposes this system into two
subsystems, an ordinary ...
In this work, for functions that satisfy a Cauchy problem for hyperparabolic equations, we write
integral equations and solve them using the method of successive approximations.
A theorem of existence of continuously differentiable solution of a system of integro-functional
equations with partial derivatives and linearly transformed arguments is proved.
We study a system of linear singularly perturbed functional differential equations by the method
of integral manifolds. We construct a change of variables that decomposes this system into two
subsystems, an ordinary ...
By using the method of the Green – Samoilenko function, an invariant torus is constructed
for a system of discrete equations which are defined on tori in the space of bounded number
sequences. Sufficient conditions are ...
In this paper we investigate the existence of a positive solution of a second order singular Sturm –
Liouville boundary-value problem, by constructing upper and lower solutions and combined
them with properties of the ...
We study a system of linear singularly perturbed functional differential equations by using the
method of integral manifolds. We construct a change of variables that decomposes this system
into two subsystems: ordinary ...
The canonical reduction method is analized in detail and applied to Maxwell and Yang–
Mills equations considered as Hamiltonian systems on some fiber bundles with symplectic and
connection structures. The minimum interaction ...
It is shown that the application of the model of the hydrogen atom, which is based on the theory
of the elliptic oscillator, makes it possible to describe the structure of electron orbits. The investigation is based on ...
We prove that a sufficient condition for stochastic Ito systems to be exponentially dichotomous
on the semiaxis is that the nonhomogeneous system havemean square bounden solutions.
The notion of the generalized amplitude modulation of oscillations and waves is introduced. The
inverse Scattering Transform Method is used to investigate the problem of generalized amplitude modulation for the Korteweg ...
With the use of the numerical-analytic method of A.M. Samoilenko and a modification of
Newton’s method, we construct an approximation to the periodical solution of a difference
equation in pertially ordered Banach spaces ...
The mechanical system consisting of a circular cylindrical shell and a rigid body attached to one
of the shell ends is considered. In linear statements, the boundary-value problem on a stressedlydeformed state of this ...
A session of the mathematical commission of the T.H. Shevchenko Scientific Society (SSS)
was held on March 16 – 17, 2001 at the I. Franko L’viv National University. The session was organized both by the mathematical ...
The characteristic initial value problem has been studied for the second order nonlinear
differential equation, and modifications of the two-sided method of its approximate integration
have been constructed.
Nguen Van Dao; Nguyen Van Dinh; Tran Kim Chi(Нелінійні коливання, 2001)
This paper deals with the Van der Pol oscillator subjected to complicated excitations. Section 1
presents the Van der Pol oscillator with a variable friction force . Section 2 is concerned with a
Van der Pol oscillator ...
We present conditions ensuring the existence of a solution in the class C¹ ([0, T]) for the singular periodic boundary-value problem (r(x' ))' = H(p(t) + q(x))k(x')f(t, x, x'(0) = x(T),
x'(0) = x'(T).
A form of some sets of quadratic forms having a sign-fixed derivative by virtue of the linear
extension of the dynamical system on a torus is proposed. The problem of comparison of
different sets with each other is investigated.
The problem of integrating the Laplace equation in a changing 3-dimensional region, with the
initial and boundary conditions, is investigated. The paper is mainly devoted to the problem
arising in dynamics of an inviscid ...