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Start Over Subject differential inequalities

1. Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Creator:
Bravyi, E,, Hakl, Robert, and Lomtatidze, Alexander
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
linear functional differential equations, Cauchy problem, existence and uniqueness, and differential inequalities
Language:
English
Description:
Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb R)\rightarrow L(I,\mathbb R)$ is a linear bounded operator, $q\in L(I,\mathbb R)$, and $c\in \mathbb R$, are established.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. 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:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public