Related papers: One class of linear Fredholm integral equations wi…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
We show that layer potential groupoids for conical domains constructed in an earlier paper (Carvalho-Qiao, Central European J. Math., 2013) are Fredholm groupoids, which enables us to deal with many analysis problems on singular spaces in a…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The…
We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. The construction covers cases where non-integer powers of $z$ and also terms containing…
We consider the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) that makes the conversion of second-class constraints into first-class ones for the case of nonlinear theories. We first present a general analysis of an attempt to…
The main purpose of this work is to provide the general solutions of a class of linear functional equations. Let $n\geq 2$ be an arbitrarily fixed integer, let further $X$ and $Y$ be linear spaces over the field $\mathbb{K}$ and let…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving…
In this work it is introduced the notion of regular Fredholm pair, i.e. a Fredholm pair whose operators are regular. The main properties of these objects are studied, and what is more, they are entirely classified. Furthermore, the index of…
We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…
In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
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…
We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…
Five essential spectra of linear relations are defined in terms of semi-Fredholm properties and the index. Basic properties of these sets are established and the perturbation theory for semi-Fredholm relations is then applied to verify a…