Related papers: Solutions to the First Order Difference Equations …
We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmetries. The results are based on a relation between…
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…
We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is a first-order sentence which characterizes this field within the class up to…
We investigate and derive second solutions to linear homogeneous second-order difference equations using a variety of methods, in each case going beyond the purely formal solution and giving explicit expressions for the second solution. We…
We propose an integral transform, called metamorphism, which allow us to reduce the order of a differential equation. For example, the second order Helmholtz equation is transformed into a first order equation, which can be solved by the…
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders…
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…
While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the…
We present an algorithm to analyze numerically the bounce solution of first-order phase transitions. Our approach is well suited to treat phase transitions with several fields. The algorithm consists of two parts. In the first part the…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
This paper focuses on resolution in linguistic first order logic with truth value taken from linear symmetrical hedge algebra. We build the basic components of linguistic first order logic, including syntax and semantics. We present a…
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.…
We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
A field k is called anti-Mordellic if every smooth curve over k with a k-point has infinitely many k-points. We prove that for a function field over an anti-Mordellic field, the subfield of constants is defined by a certain universal first…