Periodic moving waves on 2D lattices with nearest-neighbor interactions

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.Вивчено питання існування періодичних рухомих хвиль на двовимірних періодично збурених ґратках із лінійним зчепленням між найближчими частинками та з періодичними нелінійними потенціалами підкладинки. Такі дискретні системи можуть моделювати молекули, що адсорбуються на кристалічну поверхню підкладинки

Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices

We represent a solution of an inhomogeneous second-order differential equation with two delays by using matrix functions under the assumption that the linear parts are given by permutable matrices.Зображення розв’язку задачi кошi для коливної системи з двома запiзнюваннями та переставними матрицям

Some Applications of the Extended Bendixson-Dulac Theorem

During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work is to present an unified approach of some of these results, together with their corresponding proofs. We also provide several applications.Comment: 19 pages, 3 figure

Hermite–Hadamard-type inequalities for r-convex functions based on the use of Riemann–Liouville fractional integrals

By using two fundamental fractional integral identities, we deduce some new Hermite–Hadamard-type inequalities for differentiable r-convex functions and twice-differentiable r-convex functions involving Riemann–Liouville fractional integrals.Iз використанням двох фундаментальних дробових iнтегральних тотожностей отримано новi нерiвностi типу Ермiта – Адамара для диференцiйовних r-опуклих функцiй та двiчi диференцiйовних r-опуклих функцiй, що мiстять дробовi iнтеграли Рiмана – Лiувiлля

Travelling waves in nonlinear magneto-inductive lattices

We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results of periodic travelling waves of the system are presented. Our analytical results are found to be in good agreement with direct numerical computations