Nonoscillation and disconjugacy of systems of linear differential equations

Nonoscillation and disconjugacy of systems of linear differential equations

The differential equations under consideration are of the form (1) §f = A(t)x, where A(t) is a piecewise continuous real nxn-matrix on a real interval a, and the vector x = (x-j...,x ) is continuous on a. The equation is said to be nonoscillatory on a if every nontrivial real solution vector x has at least one component xv which does not vanish on a. The principal concern of this paper is the d...

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...

Oscillation and Nonoscillation Criteria for Second-order Linear Differential Equations

Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established. 1. Statement of the Problem and Formulation of Basic Results Consider the differential equation u′′ + p(t)u = 0, (1) where p : [0, +∞[→ [0, +∞[ is an integrable function. By a solution of equation (1) is understood a function u : [0,+∞[→] − ∞, +∞[ which is locally absolutely continuous tog...

K-component Disconjugacy for Systems of Ordinary Differential Equations

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...