Related papers: Linearizability Criteria for a Class of Third Orde…
In this paper we give full classification of rank 3 line arrangements in $\mathbb P^2$ (over a field of characteristic 0) that have a minimal logarithmic derivation of degree 3. The classification presents their defining polynomials, up to…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
The linearization problem by use of the Cartan equivalence method for scalar third-order ODEs via point transformations was solved partially in [1,2]. In order to solve this problem completely, the Cartan equivalence method is applied to…
A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For given evaluation point and equation parameters the memory requirement scales linearly with precision $P$, and the number…
The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…
In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…
The linearization problem of a second-order ordinary differential equation by the generalized Sundman transformation was considered earlier by Duarte, Moreira and Santos using the Laguerre form. The results obtained in the present paper…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
In this paper we use the comparison method for investigation of first order polynomial differential equations. We prove two comparison criteria for these equations. The proved criteria we use to obtain some global solvability criteria for…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
In this note, we present an extension to second order nonlinear ordinary differential equations (ODEs) of the Nagumo-like uniqueness criterion for first order ODEs established in [A. Constantin, On Nagumo's theorem, Proc. Japan Acad. 86(A)…
Using the symmetry approach, we find a class of integrable nonlinear PDEs with dispersion law $\omega(k)=k^{\frac32}$. All these equations turn out to be linearizable by means of a differential parametrization.
We compute the second and third levels of the Lasserre hierarchy for the spherical finite distance problem. A connection is used between invariants in representations of the orthogonal group and representations of the general linear group,…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
An observability problem for linear autonomous distributed systems in the class of linear operations is considered. A criterion of observability with respect to terminal state has been proved. A connection with observability with respect to…
We consider a family of higher-order Boussinesq equations with an arbitrary nonlinearity. We determine the classes of equations so that a certain type of Lie symmetry algebra is admitted in this family. In case of a quadratic nonlinearity…