Periodic weak solutions for a classical one-dimensional isotropic biquadratic Heisenberg spin chain

In this paper, we consider the model proposed by Lakshmanan, Porsezian and Daniel [M. Lakshmanan, K. Porsezian, M. Daniel, Effect of discreteness on the continuum limit of the Heisenberg spin chain, Phys. Lett. A 133 (1988) 483-488] describing the continuum isotropic biquadratic Heisenberg spin chain in one dimensional case. Following the results of integrability in [K. Porsezian, M. Daniel, M. Lakshmanan, On the integrability aspects of the one-dimensional classical continuum isotropic Heisenberg spin chain, J. Math. Phys. 33 (5) (1992) 1807-1816], we prove the existence of periodic weak solutions to this model.     

On a new method of Markov chain reduction

The practical usefulness of Markov models and Markovian decision process has been severely limited due to their extremely large dimension. Thus, a reduced model without sacrificing significant accuracy can be very interesting.

The homogeneous finite Markov chain's long-run behaviour is given by the persistent states, obtained after the decomposition in classes of connected states. In this paper we expound a new reduction method for ergodic classes formed by such persistent states. An ergodic class has a steady-state independent of the initial distribution. This class constitutes an irreducible finite ergodic Markov chain, which evolves independently after the capture of the event.

The reduction is made according to the significance of steady-state probabilities. For being treatable by this method, the ergodic chain must have the Two-Time-Scale property.

The presented reduction method is an approximate method. We begin with an arrangement of irreducible Markov chain states, in decreasing order of their steady state probability's size. Furthermore, the Two-Time-Scale property of the chain enables us to make an assumption giving the reduction. Thus, we reduce the ergodic class only to its stronger part, which contains the most important events having also a slower evolution. The reduced system keeps the stochastic property, so it will be a Markov chain     

Periodic solutions for a degenerate parabolic equation

In this work, we establish the existence of nontrivial nonnegative periodic solutions for a class of degenerate parabolic equations with nonlocal terms. The key is the using of Moser’s iteration technique and the theory of the Leray–Schauder degree.     

Periodic solutions for a class of epidemic equations

Periodic solutions for a class of delay integral equations modeling epidemics are shown to bifurcate from the identically zero solution when a certain parameter exceeds a threshold. The equations are a special case of a general model proposed by Hoppensteadt and Waltman [3]. A global bifurcation theorem of Roger Nussbaum [5] is the main tool.     

Periodic solutions for a weakly dissipated hybrid system

We consider the motion of a stretched string coupled with a rigid body at one end and we study the existence of periodic solution when a periodic force f acts on the body. The main difficulty of the study is related to the weak dissipation that characterizes this hybrid system, which does not ensure a uniform decay rate of the energy. Under additional regularity conditions on f, we use a perturbation argument in order to prove the existence of a periodic solution. In the last part of the paper we present some numerical simulations based on the theoretical results.     

Periodic solutions for a quasilinear non-autonomous second-order system

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.     

Periodic solutions for a nonautonomous ordinary differential equation

We consider the nonautonomous differential equation of second order x^″+a(t)x−b(t)x²+c(t)x³=0, where a(t),b(t),c(t) are T-periodic functions. This is a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of at least two positive T-periodic solutions for this equation, using coincidence degree theories.     

Periodic solutions for a class of superquadratic Hamiltonian systems

We prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second-order Hamiltonian systems by applying condition ^∗(C) to critical point theory, and some new solvability conditions of nontrivial periodic solutions are obtained.     

On explicit solutions of a two-echelon supply chain coordination game

A contracting game under asymmetric information specific to two-echelon supply chain coordination between a retailer of unknown type and a supplier is studied. When the parameter which is private information to the retailer (holding cost) is known up to an interval of uncertainty, a uniform discrete approximation for retailer types leads to closed-form solutions where the joint (coordinated) optimal order quantity for a modified holding cost plays a major role. Furthermore, the closed-form solutions result in increasing information rent for higher types under easy-to-verify conditions involving strict lower limits on the total holding costs of retailer and supplier and the difference between uncoordinated optimal costs of consecutive retailer types.     

Periodic solutions for a kind of Liénard equation

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of T-periodic solutions for a Liénard equations with delay. An illustrative example is provided to demonstrate that the results in this paper hold under weaker conditions than existing results, and are more effective.     

Periodic solutions for a class of non-autonomous differential delay equations

By applying symplectic transformation, Floquet theory and some results in critical point theory, we establish the existence of periodic solutions for a class of non-autonomous differential delay equations, which can be changed to Hamiltonian systems.     

Periodic solutions for a class of non-autonomous second order systems

The purpose of this paper is to study the existence of periodic solutions of non-autonomous second-order systems