Eigenschaften der algebraisch- logarithmischenIntegrale nicht homogener Differentialgleichungen
Eine Bemerkung zur Lösung von Differentialgleichungen mit Parametern bei Anwendung der Lie-Reihen
estabilidad de órbitas relativistas
Exact solutions for certain nonlinear autonomous ordinary differential equations of the second order and families of two-dimensional autonomous systems.
Exact solutions of generalized Lane-Emden equations of the second kind
Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind Then we consider two types of functions and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered...
Explicit rational solutions of Knizhnik-Zamolodchikov equation
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group n. We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.
Explicit solution for Lamé and other PDE systems
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.
Explicit solutions for boundary value problems related to the operator equations
Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation are studied for the general case, even when the algebraic equation is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.
Explicit Solutions of Several Kummer's Nonlinear Differential Equations
Exponential dichotomies for linear systems with impulsive effects.