Related papers: Linear difference operators with sequence coeffici…
This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper…
In this short paper, a formula for the sequence defined by the nonhomogeneous linear difference equation with variable coefficients is presented. A connection with the homogeneous case is shown.
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…
We consider elliptic differential operators on either the entire Euclidean space $\mathbb{R}^d$ or on subsets consisting of a cube $\Lambda_L$ of integer length $L$. For eigenfunctions of the operator, and more general solutions of elliptic…
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
Existence and uniqueness theorems for quantum stochastic differential equations with nontrivial initial conditions are proved for coefficients with completely bounded columns. Applications are given for the case of finite-dimensional…
We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…
We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…
Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{n}) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-K\"{o}the spaces, then there exists a…
For a class of variational problems with linear differential operator, we obtain a convenient form of the deviation identity, i.e., the value of the distance between approximated solutions and the exact ones. We illustrate the result with…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…
A lacunary sequence is an increasing integer sequence $\theta=(k_r)$ such that $k_r-k_{r-1}\rightarrow \infty$ as $r\rightarrow \infty.$ In this article we introduce arithmetic statistically convergent sequence space $ASC$ and lacunary…
In this research article, we establish some identities and estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some lacunary difference sequence spaces defined by Orlicz function. Moreover,…
The invariance of nonlinear partial differential equations under a certain infinite-dimensional Lie algebra A_N(z) in N spatial dimensions is studied. The special case A_1(2) was introduced in J. Stat. Phys. {\bf 75}, 1023 (1994) and…
A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences…
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…
Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We study the copolynomials of $n$ variables, i.e. $K$-linear mappings from the ring of polynomials $K[x_1,...,x_n]$ into the commutative ring $K$. We prove an existence and uniqueness theorem for a linear differential equation of infinite…