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By
Matvii, O. V.; Cherevko, I. M.
3 Citations
We study the problem of the approximation of differential equations with delay by a system of ordinary differential equations. We analyze the qualitative behavior of solutions of the original system and the approximating system and construct an algorithm for the investigation of the stability of solutions of systems with delay.
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By
Boiko, M. Ya.
We obtain a criterion for the existence of a unique periodic solution of a linear twoparameter difference equation in a Banach space.
By
Loveikin, Yu.V.; Parasyuk, I. O.
2 Citations
We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case where a Liouvilleintegrable Hamiltonian system undergoes locally Hamiltonian perturbations and, simultaneously, a deformation of the symplectic structure of the phase space. We consider a new case where the deformed symplectic structure generates a nondegenerate matrix of the Poisson brackets of action variables.
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By
Marynets’, V. V.; Pyt’ovka, O. Yu.
We study a rapidly convergent modification of a twosided method for the approximate integration of a boundaryvalue problem with parameters in boundary conditions for a system of quasilinear secondorder differential equations.
By
Chuiko, S. M.; Starkova, O.V.
4 Citations
Using the leastsquares method, we construct a new iterative procedure for finding solutions of an autonomous weakly nonlinear boundaryvalue problem in the critical case in the form of a generalized Fourier polynomial expansion.
By
Shkil', M. I.
We propose an algorithm for the reduction of a singularly perturbed system of differential equations whose characteristic equation has multiple roots to a system with simple roots.
By
Wei, Li; Agarwal, R. P.; Wong, P. J. Y.
3 Citations
Using perturbation results on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present some abstract results about the existence of solutions of nonlinear Neumann elliptic systems involving the (p, q)Laplacian. The systems discussed in this paper and the method used extend and complement some previous works.
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By
Stepanenko, O.; Maistrenko, Yu.; Yousefi, S.
We study an Ndimensional dynamical system that defines interacting economic models (a socalled quantitysetting oligopoly). Parameter regions of stability of the Nash equilibrium are obtained, and the phase diagram for the stability of the synchronized motion is investigated. We also consider the problem of cluster formation. In particular, the 2cluster state is studied extensively. A locally stable Nash equilibrium and quasiperiodic motions are present in this state. The regions of stability and the bifurcations of stable trajectories are investigated, and the corresponding bifurcation diagram is obtained.
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