Related papers: Existence and Asymptotics of Abstract Functional D…
In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
We show that the there exists an algebraic rate of convergence of solutions of finite-difference approximations for uniformly elliptic Isaacs in smooth bounded domains.
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…
Some results are proved concerning asymptotic and deficient values in connection with the second order linear differential equation $y'' + Ay = 0$, in which the coefficient $A$ is entire.
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
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…
We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such…
Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…
A correct high-energy asymptotic form of Faddeev type few-body integral equations is found. Iterative series corresponding to these asymptotic relations converge with a certain accuracy to a finite sum, which satisfies the corresponding…
A multi-linear variable separation approach is developed to solve a differential-difference Toda equation. The semi-discrete form of the continuous universal formula is found for a suitable potential of the differential-difference Toda…
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…
The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…