Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 255-279
Periodic solutions are studied for second-order differential equations with generalized forcing. Analytical bifurcation results are derived with application to forced harmonic and Duffing oscillators.
Hermite-Hadamard-type inequalities for r-convex functions using Riemann-Liouville fractional integrals
Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 175-191
By using two fundamental fractional integral identities, we derive some new Hermite – Hadamard-type inequalities for differentiable r-convex functions and twice-differentiable r-convex functions involving Riemann – Liouville fractional integrals.
Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices
Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 58-69
We represent a solution of a nonhomogeneous second-order differential equation with two delays using matrix functions under the assumption that the linear parts are given by permutable matrices.
Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 127–139
We study the existence of periodic moving waves on two-dimensional periodically forced lattices with linear coupling between nearest particles and with periodic nonlinear substrate potentials. Such discrete systems can model molecules adsorbed on a substrate crystal surface.