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