Related papers: Another Proof of Darboux's Theorem
We investigate solvability of a continuous Dirichlet boundary value problem together with its classical discretization using a gobal diffeomorphism theorem.
This paper provides a rigorous and gap-free proof of the index theorem used in the theory of regular economy. In the index theorem that is the subject of this paper, the assumptions for the excess demand function are only several usual…
In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and…
This article examines differentiability properties of the value function of positioning choice problems, a class of optimisation problems in finite-dimensional Euclidean spaces. We show that positioning choice problems' value function is…
We study the integrability in the Liouville sense of natural Hamiltonian systems with a homogeneous rational potential $V(\vq)$. Strong necessary conditions for the integrability of such systems were obtained by an analysis of differential…
We present two results on generalized Darboux properties of additive real functions. The first results deals with a weak continuity property, called ${\bf Q}$-continuity, shared by all additive functions. We show that every ${\bf…
Liouville closed $H$-fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order $1$ has a nontrivial solution. (The introduction gives a precise…
The paper proves that all power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on every closed interval. Hensel's Lemma for restricted power series is the main tool of the proof.
In this paper, we obtain a version of Ekeland's variational principle for interval-value functions by means of the Dancs-Hegedus-Medvegyev theorem [14]. We also derive two versions of Ekeland's variational principle involving the…
We develop method that allows to derive reductions and solutions to hyperbolic systems of partial differential equations. The method is based on using functions that are constant in the direction of characteristics of the system. These…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function. This theory combines the tempered fractional calculus with the…
Using the Feferman-Vaught Theorem, we prove that a definable subset of a product structure must be a Boolean combination of open sets, in the product topology induced by giving each factor structure the discrete topology. We prove a…
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…
We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…
We connect certain continuous motions of discrete planar curves resulting in semi-discrete potential Korteweg-de Vries (mKdV) equation with Darboux transformations of smooth planar curves. In doing so, we define infinitesimal Darboux…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
The classical spectral theorem completely describes self-adjoint operators on finite dimensional inner product vector spaces as linear combinations of orthogonal projections onto pairwise orthogonal subspaces. We prove a similar theorem for…
We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the…
A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and dressing methods. This transformation is used to find the exact expressions for soliton solutions on zero and…