Related papers: Linear difference operators with sequence coeffici…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
We consider semilinear elliptic second-order partial differential inequalities of the form Lu +|u|q-1u < and = Lv +|v|q-1v (*) in the whole space Rn, where n > and = 2, q > 0 and L is a linear elliptic second-order partial differential…
Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…
The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
We provide a numerical method to determine the critical lengths of linear differential operators with constant real coefficients. The need for such a procedure arises when the orders increase. The interest of this article is clearly on the…
The concept of determinant for a linear operator in an infinite-dimensional space is addressed, by using the derivative of the operator's zeta-function (following Ray and Singer) and, eventually, through its zeta-function trace. A little…
There are many methods for finding a particular solution to a nonhomogeneous linear ordinary differential equation (ODE) with constant coefficients. The method of undetermined coefficients, Laplace transform method and differential operator…
The problem of equivalency for linear differential operators of the first order is discussed.
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence,…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
We pursue the study of one-dimensional symmetry of solutions to nonlinear equations involving nonlocal operators. We consider a vast class of nonlinear operators and in a particular case it covers the fractional $p-$Laplacian operator. Just…
We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.
In this article we study the existence, continuation and bifurcation from infinity of nonconstant solutions for a nonlinear Neumann problem. We apply the Leray-Schauder degree and the degree for SO(2)-equivariant gradient operators defined…
Disproving a conjecture of Bleicher and Erd\H{o}s, we show that there exists a lacunary sequence of positive integers such that finite sums of reciprocals of its terms attain all rational numbers from a non-empty open interval. We also…