Conditions for the integrability of a second order nonlinear differential equation.
Conditions for the Integrability of Second Order Nonlinear Differential Equation, II
Consequences of the meromorphic equivalence of standard matrix differential equations.
In this article we investigate the question [of] how meromorphic differential equations can be simplified by meromorphic equivalence. In the case of equations of block size 1, which generalizes the case of distinct eigenvalues, we identify a class of equations which are simplest possible in the sense that they carry the smallest number of parameters whithin their equivalence classes. We also discuss conditions under which individual equations can be simplified. Particular attention is paid to the...
Constant invariant solutions of the Poincaré center-focus problem.
Constructive solution of coupled second order delay differential equations with variable coefficients.
Corrections to the paper: “On formal theory of differential equations. II.”
Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems
In this paper we obtain existence conditions and a closed form of the general solution of higher order singular regular boundary value problems. The approach is based on the concept of co-solution of algebraic matrix equations of polynomial type that permits the treatment of the problem without considering an extended first order system as it has been done in the known literature.
Criterion for the polynomial solutions of certain first order differential equations
Cylindrical Tzitzeica curves implies forced harmonic oscillators.
Die Anwendung der Quasilinearisation auf gewisse Probleme aus der Theorie der gewöhnlichen Differentialgleichungen 3. Ordnung
Differential equations on the plane with given solutions.
The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.
Du facteur intégrant pour les expressions différentielles du premier ordre renfermant un nombre quelconque de variables indépendantes
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.
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