Related papers: Non-homogeneous Linear Set-Valued Differential Equ…
The expressions of solutions for general $n\times m$ matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…
In this paper, we mainly focus on the set-valued (stochastic) analysis on the space of convex, closed, but possibly unbounded sets, and try to establish a useful theoretical framework for studying the set-valued stochastic differential…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
In this work, an exact solution to a new generalized nonlinear KdV partial differential equations has been investigated using homotopy analysis techniques. The mentioned partial differential equation has been solved using homotopy…
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis-Palamodov from…
We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
Consider the linear differential equation of $m$-th order with constant coefficients from the valuation ring $K$ of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution of this equation from…
This study shows how to obtain least-squares solutions to initial and boundary value problems to nonhomogeneous linear differential equations with nonconstant coefficients of any order. However, without loss of generality, the approach has…
By using the method developed in the paper [G.Pantsulaia, G.Giorgadze, On some applications of infinite-dimensional cellular matrices, {\it Georg. Inter. J. Sci. Tech., Nova Science Publishers,} Volume 3, Issue 1 (2011), 107-129], it is…
We study the initial boundary value problem for one-dimensional Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results on the Cauchy…
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…