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Start Over Subject functional differential equation

1. Asymptotic properties of differential equations with advanced argument

Creator:
Čermák, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, functional (nondifferential) equation, advanced argument, and asymptotic behaviour
Language:
English
Description:
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation \[ y^{\prime }(x)=ay(\tau (x))+by(x),\qquad x\in [x_0,\infty ) \] of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution $y(x)$ which behaves in this way.
Rights:
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2. Coordinate description of analytic relations

Creator:
Neuman, František
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
canonical form, Brandt groupoid, Ehresmann groupoid, transformation, differential equation, Abel functional equation, and functional differential equation
Language:
English
Description:
In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations

Creator:
Dilna, N. and Rontó, A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, Cauchy problem, initial value problem, and differential inequality
Language:
English
Description:
New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
Rights:
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4. On solvability sets of boundary value problems for linear functional differential equations

Creator:
Bravyi, Eugene
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, boundary value problem, and periodic problem
Language:
English
Description:
Consider boundary value problems for a functional differential equation ( x (n) (t) = (T +x)(t) − (T −x)(t) + f(t), t ∈ [a, b], lx = c, where T +, T − : C[a, b] → L[a, b] are positive linear operators; l: ACn−1 [a, b] → R n is a linear bounded vector-functional, f ∈ L[a, b], c ∈ ℝ n , n ≥ 2. Let the solvability set be the set of all points (T +, T −) ∈ ℝ + 2 such that for all operators T +, T − with kT ±kC→L = T ± the problems have a unique solution for every f and c. A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl, A. Lomtatidze, J. Šremr: Some boundary value problems for first order scalar functional differential equations. Folia Mathematica 10, Brno, 2002.
Rights:
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5. On the dimension of the solution set to the homogeneous linear functional differential equation of the first order

Creator:
Domoshnitsky, Alexander, Hakl, Robert, and Půža, Bedřich
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, boundary value problem, differential inequality, and solution set
Language:
English
Description:
Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.
Rights:
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6. Positivity of Green's matrix of nonlocal boundary value problems

Creator:
Domoshnitsky, Alexander
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, nonlocal boundary value problem, positivity of Green's operator, fundamental matrix, and differential inequalities
Language:
English
Description:
We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of n linear functional differential equations with the boundary conditions nixi − ∑n j=1 mijxj = βi , i = 1, . . . , n, where ni and mij are linear bounded ''local” and ''nonlocal” functionals, respectively, from the space of absolutely continuous functions. For instance, nixi = xi(ω) or nixi = xi(0) − xi(ω) and mijxj = ∫ ω 0 k(s)xj(s) ds + ∑nij r=1 cijrxj (tijr) can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator for auxiliary ''local'' problem which consists of a “close” equation and the local conditions nixi = αi , i = 1, . . . , n.
Rights:
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