Related papers: Disconjugacy of a second order linear differential…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
In this article we give, for the fist time the solution of the general difference equation of 2-degree. We also give as application the expansion of a continued fraction into series, which was first proved, found in the past by the author.
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary differential equations. Two points along a base integral curve are conjugate if there exists a non-trivial Jacobi field along that curve that…
In previous work we established a multilinear duality and factorisation theory for norm inequalities for pointwise weighted geometric means of positive linear operators defined on normed lattices. In this paper we extend the reach of the…
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…
Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…
This paper investigates the Harnack inequality for nonnegative solutions to second-order parabolic equations in double divergence form. We impose conditions where the principal coefficients satisfy the Dini mean oscillation condition in…
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
The Riccati equation method is used to establish some oscillatory criteria for the second order linear functional - differential equations of multiple terms with locally integrable coefficients. An interval oscillation criterion for the…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
Coupled second order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations we focus our attention on the…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
Second-order two-scale expansions, a unified proof for the regularity of the correctors based on the translation invariant and a lemma for extracting $O(\epsilon)$ from the remainder term are presented for the second order nonlinear…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
We derive a second-order differential equation for the two-loop sunrise graph in two dimensions with arbitrary masses. The differential equation is obtained by viewing the Feynman integral as a period of a variation of a mixed Hodge…
In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace…
The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary…