Oscillations in linear systems of differential-difference equations

Linear difference and differential equations

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Liouvillian solutions of linear difference-differential equations

For a field k with an automorphism σ and a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y ) = AY, δ(Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), σ(x) = x + 1,...

Oscillations in a Linear System of Differential-Difference Equations of Arbitrary Order

There exists an extensive amount of literature dealing with oscillations in scalar differential equations of first and higher order with and without deviating arguments and we refer to Kartsatos [4] for a survey of the work done in this area. However, almost no attention has been paid for studying oscillations in systems (non-scalar) of differential equations with deviating arguments. The purpo...

Application of the linear Differential Equations on the Plane and Elements of Nonlinear Systems, In Economics

In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. These two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. In this paper I will consider the linear differential equations on the plane (phase diagram) and elements of nonl...