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The Jacobi last multiplier for difference equations
Jacobi Last Multiplier first order lineal partial differential difference equations
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2012/2/29
We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.
Stability of nonlinear stochastic Volterra difference equations with continuous time
Nonlinear stochastic difference equations Stability Lyapunov functional construction Continuous time
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2011/11/4
In recent years, many authors investigated the systems of stochastic difference equations with discrete time or the systems of numerical solution for stochastic difference equations with continue time...
Differential-difference equations associated with the fractional Lax operators
Lax pair discretization Bogoyavlensky lattice Sawada Kotera equation Kaup Kupershmidt equation
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2011/9/30
Abstract: We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference ...
Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
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2010/12/28
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
Difference equations cluster algebras Poisson bracket for integrable difference equations
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2011/2/28
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Li-ouville equation, from the view point of the general T-s...
Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
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2011/3/4
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
On Non-point Invertible Transformations of Difference and Differential-difference Equations
Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/10
Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are ...
Positive trigonometric polynomials for strong stability of difference equations
trigonometric polynomials strong stability difference equations
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2010/11/11
We follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time ...
Dynamics of a rational system of difference equations in the plane
Dynamics difference equations
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2010/11/15
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the paramet...
Tail behavior of stationary solutions of random difference equations: the case of regular matrices
Markov renewal theory implicit renewal theory Harris recurrence
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2010/12/1
Given a sequence (Mn,Qn)n≥1 of i.i.d. random variables with generic copy (M,Q)such that M is a regular d × d matrix and Q takes values in Rd, we consider the random difference equation (RDE) Rn = MnRn...
Bohl-Perron type stability theorems for linear difference equations with infinite delay
Bounded delay uniform stability Perron’s property phase space
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2010/12/15
Relation between two properties of linear difference equations with infinite delay is inves-
tigated: (i) exponential stability, (ii) ℓp-input ℓq-state stability (sometimes is called Perr...
Galois theory of difference equations with periodic parameters
Difference Galois theory q-difference equations Jacobi’s thetafunction sequences
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2010/11/30
We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups.We then apply this to constructively test...
Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint
Differential equations difference equations algebraic relations
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2010/12/6
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ-ence equation, with coefficients in the field of rational ...
Discrete Time and Finite State Reflected Backward Stochastic Difference Equations
BSDE DF-RBSDE Comparison Theorem g-martingale mul-tiple prior martingale Knightian uncertainty
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2010/4/27
In this paper, we firstly establish the discrete time and finite state reflected backward stochastic difference equations(DF-RBSDEs for short); then we explore the corresponding basic properties and t...
Oscillation criteria for a class of partial difference equations
Oscillation Partial difference equation Continuous variables
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2010/9/10
In this paper we consider the partial difference equation with continuous
variables, Some sufficient conditions for all solutions of this equation
to be oscillatory are obtained.