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Parallelisms between differential and difference equations

Veronika Chrastinová, Václav Tryhuk (2012)

Mathematica Bohemica

The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.

Particular solutions for a class of ODE related to the $L$ -exponential functions.

Bretti, Gabriella, Natalini, Pierpaolo (2004)

Georgian Mathematical Journal

Polynomial algebra of constants of the Lotka-Volterra system

Jean Moulin Ollagnier, Andrzej Nowicki (1999)

Colloquium Mathematicae

Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form $d = x (C y + z) \frac{\partial}{\partial x} + y (A z + x) \frac{\partial}{\partial y} + z (B x + y) \frac{\partial}{\partial z}$ , called the Lotka-Volterra derivation, where A,B,C ∈ k.

Displaying 1 – 8 of 8

Parallelisms between differential and difference equations

Particular solutions for a class of ODE related to the $L$ -exponential functions.

Polynomial algebra of constants of the Lotka-Volterra system

Polynomial solutions of a generalization of the first Painlevé differential equation.

Positive solutions for singular three-point boundary-value problems.

Power series techniques for a special Schrödinger operator and related difference equations.

Poznámka k integrování některých differenciálních rovnic lineárních

Properties of solutions of the differential equation xx'' - kx'...+ f(x) = 0.

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