Related papers: Modular differential equations and algebraic syste…
Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of…
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. Such a family contains the…
The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on an iterative procedure…
The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…
We consider a class of $n^{\text{th}}$-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of $u$. We demonstrate…
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving…
We prove the existence of a universal family over every component of the moduli space of marked irreducible holomorphic symplectic manifolds. The analogous result follows for the Teichmuller spaces.
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
It is well-known that any solution of the Laplace equation is a real or imaginary part of a complex holomorphic function. In this paper, in some sense, we extend this property into four order hyperbolic and elliptic type PDEs. To be more…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
In this paper differential operators on various moduli spaces (e.g. of holomorphic vector bundles) are described in a canonical way in terms of the geometry of a certain distinguished completion of an appropriate configuration space.
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.
We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that…