For a system of ordinary differential equations depending on a small parameter, defined on the direct product of a torus and aEuclidean space, and subjected to impulsive action on a submanifold of codimension 1 of the ...
We consider a family of systems of differential equations depending on a sufficiently small parameter
with zero value of which we obtained a couple of independent systems. We used the method of Green –
Samoilenko function ...
The minimality of a nonautonomous dynamical system given by a compact Hausdorff space X and a
sequence of continuous selfmaps of X is studied. A sufficient condition for nonminimality of such a
system is formulated. A ...
We study exponential dichotomy for a linear quasiperiodic system with impulses. The piecewise smoothness of separatrix manifolds is proved. For nonlinear quasiperiodic impulsive system with linearized system that posseses ...
In this paper, an existence result for a nonlinear n-th order ordinary random differential equation is proved
under Caratheodory condition. Two existence results for extremal random solutions are also proved for ´
Caratheodory ...
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 ...
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.
We consider the Hill’s equation with damping describing the parametric oscillations of the torsional pendulum excited by means of varying the moment of inertia of the rotating body. Using the method of a small
parameter ...
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 establish new efficient conditions sufficient for the unique solvability of the Cauchy problem for twodimensional systems of linear functional differential equations with monotone operators.
In the present paper, we propose new sufficient conditions for the existence of periodic solutions for a class of Rayleigh type p-Laplacian equation with deviating arguments. Results obtained complement or improvethe ...
Some aspects of the description of Lagrangian and Hamiltonian formalisms naturally arising from the
invariance structure of given nonlinear dynamical systems on the infinite-dimensional functional manifold is presented. ...
Aguerrea, M.; Valenzuela, G.(Нелінійні коливання, 2010)
In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling
waves for non-local delayed reaction-diffusion equation.
Rontó, M.; Shchobak, N.M.(Нелінійні коливання, 2003)
We consider a parametrized boundary-value problem containing an unknown parameter both in the nonlinear ordinary differential equations and in the nonlinear boundary conditions. By using a suitable change
of variables, ...
The aim of this paper is to study the asymptotic properties and oscillation of the n-th order delay differential equation
r(t)[x⁽ⁿ⁻¹⁾(t)]γ)+ q(t)f(x(τ (t))) = 0.
The results obtained are based on some new comparison ...
The generalized characteristics method is developed in the framework of the geometric Monge picture. The
Hopf – Lax-type extremality solutions to a wide class of Cauchy problem for nonlinear partial differential equations ...