The continuous q-Hermite polynomials, or the wave functions in the model of the q-harmonic oscillator under consideration, satisfy two

difference equations.

Linear stochastic

difference equations derive from mathematical model (1) of IPMSM:

Dynamics of second order rational

difference equations with open problem and conjectures.

For

difference equations there will be studied such issues as solvability, equilibrium existence and stability.

These include describing first-order linear vector stochastic

difference equations as the building block for a class of economic structures with competitive equilibrium prices and quantities; and explaining fast algorithms, like the doubling algorithm, for computing the value function and optimal decision rule of social planning problems.

They include projects, bifurcation diagrams and life history tables, applied problems, historical information, and representations of topics visually, numerically, algebraically, and verbally, and place sequences,

difference equations, and their applications in early chapters.

Agarwal,

Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York, 1992.

The theory of finite

difference equations and their wide applications has drawn much attention in the past few decades.

The Lyapunov inequality and many of its generalizations have proved to be useful tools in oscillation theory, disconjugacy, eigenvalue problems, and numerous other applications for the theories of differential and

difference equations and also in time scales.

Recently, there have been considerable activities to develop the theory of dynamic equations on time scales as this theory unifies the theories of differential and finite

difference equations.

Among his topics are combinatorics, recurrences or

difference equations, enumeration with generating functions, and asymptotics and generating functions.

Periodic Solutions of

Difference Equations and Orbital Stability